Waves

In an experiment to determine the velocity of sound in air at room temperature using a resonance tube, the first resonance is observed when the air column has a length of 20.0 cm for a tuning fork of frequency 400 Hz is used. The velocity of the sound at room temperature is 336 ms$^{-1}$. The third resonance is observed when the air column has a length of ______ cm

Which of the following equations correctly represents a travelling wave having wavelength $\lambda=4.0$ cm, frequency $\nu=100$ Hz and travelling in positive $x$-axis direction ?

An employee of a factory moving away from his workplace by a car listens to the siren of the factory. He drives the car at the speed of 72 kmh$^{-1}$ in the direction of wind which is blowing at 72 kmh$^{-1}$ speed. Frequency of siren is 720 Hz. The employee hears an apparent frequency of ______ Hz.

(Assume speed of sound to be 340 ms$^{-1}$)

An observer is riding on a bicycle and moving towards a hill at 18 kmh$^{-1}$. He hears a sound from a source at some distance behind him directly as well as after its reflection from the hill. If the original frequency of the sound as emitted by source is 640 Hz and velocity of the sound in air is 320 m/s, the beat frequency between the two sounds heard by observer will be ______ Hz.

Sound travels in a mixture of two moles of helium and n moles of hydrogen. If rms speed of gas molecules in the mixture is $\sqrt2$ times the speed of sound, then the value of n will be :

When a car is approaching the observer, the frequency of horn is 100 Hz. After passing the observer, it is 50 Hz. If the observer moves with the car, the frequency will be $\dfrac x3$ Hz where $x=$ ______.

A transverse wave is represented by $y=2\sin(\omega t-kx)$ cm. The value of wavelength (in cm) for which the wave velocity becomes equal to the maximum particle velocity, will be :

A wire of length 30 cm, stretched between rigid supports, has it's n$^{\text{th}}$ and (n+1)$^{\text{th}}$ harmonics at 400 Hz and 450 Hz, respectively. If tension in the string is 2700 N, it's linear mass density is ______ kg/m.

In the wave equation

$$y=0.5\sin\frac{2\pi}\lambda(400t-x)\text{ m}$$

the velocity of the wave will be :

The frequency of echo will be ______ Hz if the train blowing a whistle of frequency 320 Hz is moving with a velocity of 36 km/h towards a hill from which an echo is heard by the train driver. Velocity of sound in air is 330 m/s.

The speed of a transverse wave passing through a string of length 50 cm and mass 10 g is 60 m s$^{-1}$. The area of cross-section of the wire is 2.0 mm$^2$ and its Young's modulus is $1.2\times10^{11}$ N m$^{-2}$. The extension of the wire over its natural length due to its tension will be $x\times10^{-5}$ m. The value of $x$ is _______.

A source, approaching with speed $u$ towards the open end of a stationary pipe of length $L$, is emitting a sound of frequency $f_s$. The farther end of the pipe is closed. The speed of sound in air is $v$ and $f_0$ is the fundamental frequency of the pipe. For which of the following combination(s) of $u$ and $f_s$, will the sound reaching the pipe lead to a resonance?

A stationary tuning fork is in resonance with an air column in a pipe. If the tuning fork is moved with a speed of $2\ \mathrm{m\,s^{-1}}$ in front of the open end of the pipe and parallel to it, the length of the pipe should be changed for the resonance to occur with the moving tuning fork. If the speed of sound in air is $320\ \mathrm{m\,s^{-1}}$, the smallest value of the percentage change required in the length of the pipe is ______.

A train S1, moving with a uniform velocity of 108 km/h, approaches another train S2 standing on a platform. An observer O moves with a uniform velocity of 36 km/h towards S2, as shown in figure. Both the trains are blowing whistles of same frequency 120 Hz. When O is 600 m away from S2 and distance between S1 and S2 is 800 m, the number of beats heard by O is ______.

[Speed of the sound = 330 m/s]

If the tension in each string is $T_0$, the correct match for the highest fundamental frequency in $f_0$ units will be,

The length of the strings 1, 2, 3 and 4 are kept fixed at $L_0$, $\dfrac{3L_0}2$, $\dfrac{5L_0}4$, and $\dfrac{7L_0}4$, respectively. Strings 1, 2, 3, and 4 are vibrated at their 1st, 3rd, 5th, and 14th harmonics, respectively such that all the strings have same frequency. The correct match for the tension in the four strings in the units of $T_0$ will be,

Two men are walking along a horizontal straight line in the same direction. The man in front walks at a speed $1.0\ \mathrm{m\,s^{-1}}$ and the man behind walks at a speed $2.0\ \mathrm{m\,s^{-1}}$. A third man is standing at a height 12 m above the same horizontal line such that all three men are in a vertical plane. The two walking men are blowing identical whistles which emit a sound of frequency 1430 Hz. The speed of sound in air is $330\ \mathrm{m\,s^{-1}}$. At the instant, when the moving men are 10 m apart, the stationary man is equidistant from them. The frequency of beats in Hz, heard by the stationary man at this instant, is ______.

In an experiment to measure the speed of sound by a resonating air column, a tuning fork of frequency 500 Hz is used. The length of the air column is varied by changing the level of water in the resonance tube. Two successive resonances are heard at air columns of length 50.7 cm and 83.9 cm. Which of the following statements is (are) true?

A block $M$ hangs vertically at the bottom end of a uniform rope of constant mass per unit length. The top end of the rope is attached to a fixed rigid support at $O$. A transverse wave pulse (Pulse 1) of wavelength $\lambda_0$ is produced at point $O$ on the rope. The pulse takes time $T_{OA}$ to reach point $A$. If the wave pulse of wavelength $\lambda_0$ is produced at point $A$ (Pulse 2) without disturbing the position of $M$ it takes time $T_{AO}$ to reach point $O$. Which of the following options is/are correct?

A stationary source emits sound of frequency $f_0 = 492$ Hz. The sound is reflected by a large car approaching the source with a speed of $2\ \mathrm{ms^{-1}}$. The reflected signal is received by the source and superposed with the original. What will be the beat frequency of the resulting signal in Hz? (Given that the speed of sound in air is $330\ \mathrm{ms^{-1}}$ and the car reflects the sound at the frequency it has received).