Waves Practice Questions

A steel wire with mass per unit length $7.0 \times 10^{-3} {\text{kg}}$ ${\text{m}}^{-1}$ is under tension of $70 {\text{N}}$. The speed of transverse waves in the wire will be: [1-Feb-2023 Shift 1]

The displacement equations of two interfering waves are given by$y_1=10 sin \; (\omega t+\;\frac{\pi }{3}) {\text{cm}},$ $y_2=5[ sin \;\omega t+{\sqrt{3}} \cos \omega t] {\text{cm}} \;\text{ respectively. }\;$The amplitude of the resultant wave is ____${\text{cm}}$. [31-Jan-2023 Shift 2]

For a periodic motion represented by the equation $y= sin \;\omega {\text{t}}+\cos \omega {\text{t}}$ the amplitude of the motion is [10-Apr-2023 shift 2]

A tunning fork of frequency $340 {\text{Hz}}$ resonates in the fundamental mode with an air column of length $125 {\text{cm}}$ in a cylindrical tube closed at one end. When water is slowly poured in it, the minimum height of water required for observing resonance once again is _____cm.(Velocity of sound in air is $340 {\text{ms}}^{-1}$ ) [28-Jun-2022-Shift-2]

In the wave equation $y-0.5 \sin \;\frac{2 \pi }{\lambda }(400 {\text{t}}-x) {\text{m}}$ the velocity of the wave will be: [28-Jul-2022-Shift-1]

The first overtone frequency of an open organ pipe is equal to the fundamental frequency of a closed organ pipe. If the length of the closed organ pipe is $20 {\text{cm}}$. The length of the open organ pipe is ______cm. [25-Jun-2022-Shift-1]

Which of the following equations correctly represents a travelling wave having wavelength $\lambda =4.0 {\text{cm}}$, frequency ${\text{v}}=100 {\text{Hz}}$ and travelling in positive $x$-axis direction? [30-Jun-2022-Shift-1]

A set of 20 tuning forks is arranged in a series of increasing frequencies. If each fork gives 4 beats with respect to the preceding fork and the frequency of the last fork is twice the frequency of the first, then the frequency of last fork is _____ ${\text{Hz}}$ [26-Jun-2022-Shift-2]

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 ${Hz}$. [25-Jul-2022-Shift-1]

A wire of length $30 {\text{cm}}$, stretched between rigid supports, has it's $n^{\;\text{th }\;}$ and $(n+1)^{\;\text{th }\;}$ harmonics at 400 ${\text{Hz}}$ and $450 {\text{Hz}}$, respectively. If tension in the string is $2700 {\text{N}}$, it's linear mass density is _________ ${\text{kg}} / {\text{m}}$. [27-Jul-2022-Shift-2]

A transverse wave is represented by $y=2 \sin (\omega t-k x) {\text{cm}}$. The value of wavelength (in ${\text{cm}}$ ) for which the wave velocity becomes equal to the maximum particle velocity, will be : [26-Jul-2022-Shift-2]

Two travelling waves of equal amplitudes and equal frequencies move in opposite directions along a string. They interfere to produce a stationary wave whose equation is given by $y=(10 \cos \pi x \sin \;\frac{2 \pi t}{T}) {\text{cm}}$The amplitude of the particle at $x=\;\frac{4}{3} {\text{cm}}$ will be _____${\text{cm}}$. [24-Jun-2022-Shift-2]

The frequency of echo will be _______ ${\text{Hz}}$ if the train blowing a whistle of frequency $320 {\text{Hz}}$ is moving with a velocity of $36 {\text{km}} / {\text{h}}$ towards a hill from which an echo is heard by the train driver. Velocity of sound in air is $330 {\text{m}} / {\text{s}}$. [28-Jul-2022-Shift-1]

The equations of two waves are given by:$y_1=5 \sin 2 \pi (x-v t) {\text{cm}}$ $y_2=3 \sin 2 \pi (x-v t+1.5) {\text{cm}}$These waves are simultaneously passing through a string. The amplitude of the resulting wave is: [24-Jun-2022-Shift-1]

When a car is approaching the observer, the frequency of horn is $100 {\text{Hz}}$. After passing the observer, it is $50 {\text{Hz}}$. If the observer moves with the car, the frequency will be $\;\frac{x}{3} {\text{Hz}}$ where $x=$ __________. [26-Jul-2022-Shift-1]

If a wave gets refracted into a denser medium, then which of the following is true? [27-Jun-2022-Shift-2]

The velocity of sound in a gas, in which two wavelengths $4.08 {\text{m}}$ and $4.16 {\text{m}}$ produce 40 beats in $12 {\text{s}}$, will be : [28-Jun-2022-Shift-1]

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 $20.0 {\text{cm}}$ for a tuning fork of frequency $400 {\text{Hz}}$ is used. The velocity of the sound at room temperature is $336 {\text{ms}}^{-1}$. The third resonance is observed when the air column has a length of ___${\text{cm}}$. [29-Jun-2022-Shift-2]