Standing Waves in Strings and Organ Pipes

Interactive Feed

JEE Main 2003

A metal wire of linear mass density of $9.8 g/m$ is stretched with a tension of $10 kg-wt$ between two rigid supports $1 m$ apart. The wire passes at its middle point between the poles of a permanent magnet and it vibrates in resonance when carrying an alternating current of frequency $n$ . The frequency $n$ of the alternating source is

50 Hz

(B)

100 Hz

(C)

200 Hz

(D)

25 Hz

JEE Main 2018

LEVELJEE Main

A granite rod of 60 cm length is clamped at its middle point and is set into longitudinal vibrations. The density of granite is $2.7 \times 1 0^{3} kg/m^{3}$ and its Young's modulus is $9.27 \times 1 0^{10} Pa$ . What will be the fundamental frequency of the longitudinal vibrations?

Two identical strings $X$ and $Z$ made of same material have tensions $T_{X}$ and $T_{Z}$ in them. If their fundamental frequencies are $450 Hz$ and $300 Hz$ respectively, then the ratio of $T_{X} / T_{Z}$ is

A string of length 1 m and mass 5 g is fixed at both ends. The tension in the string is 8.0 N. The string is set into vibration using an external vibrator of frequency 100 Hz. The separation between successive nodes on the string is close to

A closed organ pipe of length $L$ and an open organ pipe contain gases of densities $ρ_{1}$ and $ρ_{2}$ respectively. The compressibility of gases are equal in both the pipes. Both the pipes are vibrating in their first overtone with same frequency. The length of the open pipe is $\frac{x}{3} L \frac{ρ _{1}}{ρ _{2}}$ where $x$ is ...... . (Round off to the nearest integer)

LEVELJEE Main

A cylindrical tube open at both ends, has a fundamental frequency $f$ , in air. The tube is dipped vertically in water so that half of it is in water. The fundamental frequency of the air-column is now

(A)

f

(B)

f /2

(C)

\frac{3 f}{4}

(D)

2 f

JEE Main 2019

LEVELJEE Advanced

A resonance tube is old and has jagged end. It is still used in the laboratory to determine velocity of sound in air. A tuning fork of frequency $512 Hz$ produces first resonance when the tube is filled with water to a mark $11 cm$ below a reference mark near the open end of the tube. The experiment is repeated with another fork of frequency $256 Hz$ which produces first resonance when water reaches a mark $27 cm$ below the reference mark. The velocity of sound in air, obtained in the experiment is close to

(A)

328 ms^{- 1}

(B)

341 ms^{- 1}

(C)

322 ms^{- 1}

(D)

335 ms^{- 1}

JEE Main 2013

LEVELJEE Advanced

A sonometer wire of length $1.5 m$ is made of steel. The tension in it produces an elastic strain of $1%$ . What is the fundamental frequency of steel, if density and elasticity of steel are $7.7 \times 1 0^{3} kg/m^{3}$ and $2.2 \times 1 0^{11} N/m^{2}$ , respectively?

(A)

188.5 Hz

(B)

178.2 Hz

(C)

200.5 Hz

(D)

770 Hz

JEE Main 2019

LEVELJEE Main

A closed organ pipe has a fundamental frequency of $1.5 kHz$ . The number of overtones that can be distinctly heard by a person with this organ pipe will be (Assume that the highest frequency a person can hear is $20, 000 Hz$ )

A one metre long (both ends open) organ pipe is kept in a gas that has double the density of air at STP. Assuming the speed of sound in air at STP is $300 m/s$ , the frequency difference between the fundamental and second harmonic of this pipe is ...... Hz. [2020, 8 Jan Shift-I]

LEVELBoard

Length of a string tied to two rigid supports is $40 cm$ . Maximum length (wavelength in cm) of a stationary wave produced on it, is

(A)

20

(B)

80

(C)

40

(D)

120

JEE Main 2019

LEVELJEE Main

A string is clamped at both the ends and it is vibrating in its 4th harmonic. The equation of the stationary wave is $Y = 0.3 sin (0.157 x) cos (200 π t)$ . The length of the string is (All quantities are in SI units)

In a resonance tube experiment, when the tube is filled with water up to a height of $17.0 cm$ from bottom, it resonates with a given tuning fork. When the water level is raised, the next resonance with the same tuning fork occurs at a height of $24.5 cm$ . If the velocity of sound in air is $330 m/s$ , the tuning fork frequency is

(A)

1100 Hz

(B)

3300 Hz

(C)

2200 Hz

(D)

550 Hz

JEE Main 2020

LEVELJEE Main

A wire of length $L$ and mass per unit length $6.0 \times 1 0^{- 3} kgm^{- 1}$ is put under tension of $540 N$ . Two consecutive frequencies that it resonates at are : $420 Hz$ and $490 Hz$ . Then, $L$ in metres is

A pipe open at both ends has a fundamental frequency $f$ in air. The pipe is dipped vertically in water, so that half of it is in water. The fundamental frequency of the air column is now

(A)

\frac{f}{2}

(B)

\frac{3 f}{4}

(C)

2 f

(D)

f

JEE Main 2019

LEVELJEE Advanced

A wire of length $2 L$ , is made by joining two wires $A$ and $B$ of same length but different radii $r$ and $2 r$ and made of the same material. It is vibrating at a frequency such that the joint of the two wires forms a node. If the number of antinodes in wire $A$ is $p$ and that in $B$ is $q$ , then the ratio $p : q$ is

A wire of density $9 \times 1 0^{- 3} kg-cm^{- 3}$ is stretched between two clamps 1 m apart. The resulting strain in the wire is $4.9 \times 1 0^{- 4}$ . The lowest frequency of the transverse vibrations in the wire is (Young's modulus of wire, $Y = 9 \times 1 0^{10} Nm^{- 2}$ ), (to the nearest integer) ……… .

LEVELJEE Main

A string is stretched between fixed points separated by 75.0 cm. It is observed to have resonant frequencies of 420 Hz and 315 Hz. There are no other resonant frequencies between these two. Then, the lowest resonant frequency for this string is

A wave $y = a sin (ω t - k x)$ on a string meets with another wave producing a node at $x = 0$ . Then, the equation of the unknown wave is

(A)

y = a sin (ω t + k x)

(B)

y = - a sin (ω t + k x)

(C)

y = a sin (ω t - k x)

(D)

y = - a sin (ω t - k x)

JEE Main 2019

LEVELJEE Main

A tuning fork of frequency $480 Hz$ is used in an experiment for measuring speed of sound ( $v$ ) in air by resonance tube method. Resonance is observed to occur at two successive lengths of the air column $l_{1} = 30 cm$ and $l_{2} = 70 cm$ . Then, $v$ is equal to

(A)

332 ms^{- 1}

(B)

384 ms^{- 1}

(C)

338 ms^{- 1}

(D)

379 ms^{- 1}

JEE Main 2014

LEVELJEE Main

A pipe of length 85 cm is closed from one end. Find the number of possible natural oscillations of air column in the pipe whose frequencies lie below 1250 Hz. The velocity of sound in air is 340 m/s.

A string 2.0 m long and fixed at its ends is driven by a 240 Hz vibrator. The string vibrates in its third harmonic mode. The speed of the wave and its fundamental frequency is

While measuring the speed of sound by performing a resonance column experiment, a student gets the first resonance condition at a column length of $18 cm$ during winter. Repeating the same experiment during summer, she measures the column length to be $x cm$ for the second resonance. Then,

(A)

18 > x

(B)

x > 54

(C)

54 > x > 36

(D)

36 > x > 18

LEVELJEE Main

Tube $A$ has both ends open while tube $B$ has one end closed, otherwise they are identical. The ratio of fundamental frequency of tubes $A$ and $B$ is

(A)

1 : 2

(B)

1 : 4

(C)

2 : 1

(D)

4 : 1

JEE Advanced 2001

LEVELJEE Main

The ends of a stretched wire of length $L$ are fixed at $x = 0$ and $x = L$ . In one experiment the displacement of the wire is $y_{1} = A sin (\frac{π x}{L}) sin ω t$ and energy is $E_{1}$ and in other experiment its displacement is $y_{2} = A sin (\frac{2 π x}{L}) sin 2 ω t$ and energy is $E_{2}$ . Then

(A)

E_{2} = E_{1}

(B)

E_{2} = 2 E_{1}

(C)

E_{2} = 4 E_{1}

(D)

E_{2} = 16 E_{1}

A string of length 1 m and mass 5 g is fixed at both ends. The tension in the string is 8.0 N. The string is set into vibration using an external vibrator of frequency 100 Hz. The separation between successive nodes on the string is close to

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Length of a string tied to two rigid supports is 40 cm. Maximum length (wavelength in cm) of a stationary wave produced on it, is

A string is stretched between fixed points separated by 75.0 cm. It is observed to have resonant frequencies of 420 Hz and 315 Hz. There are no other resonant frequencies between these two. Then, the lowest resonant frequency for this string is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } A wave y=asin(ωt−kx) on a string meets with another wave producing a node at x=0. Then, the equation of the unknown wave is

A pipe of length 85 cm is closed from one end. Find the number of possible natural oscillations of air column in the pipe whose frequencies lie below 1250 Hz. The velocity of sound in air is 340 m/s.

A string 2.0 m long and fixed at its ends is driven by a 240 Hz vibrator. The string vibrates in its third harmonic mode. The speed of the wave and its fundamental frequency is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Tube A has both ends open while tube B has one end closed, otherwise they are identical. The ratio of fundamental frequency of tubes A and B is

Length of a string tied to two rigid supports is $40 cm$ . Maximum length (wavelength in cm) of a stationary wave produced on it, is

A wave $y = a sin (ω t - k x)$ on a string meets with another wave producing a node at $x = 0$ . Then, the equation of the unknown wave is

Tube $A$ has both ends open while tube $B$ has one end closed, otherwise they are identical. The ratio of fundamental frequency of tubes $A$ and $B$ is