MODEL QUESTIONS (IPE PATTERN)

Two progressive transverse  waves given by ${\mathrm{y}}_1=0.07 \mathrm{sin\pi }\left[12 \mathrm{x}-500\mathrm{t}\right]$and $y_2=0.07 \sin \pi \left[12 x-500t\right]$ travelling along stretched string form nodes and anti nodes. What is the displacement at the anti nodes?  What is the wavelength of the standing wave?

A string has a length of $0.4 \mathrm{m}$ and a mass of $0.16 g$. If the tension in the string is $70 \mathrm{N}$, what are three lowest frequency it produces, when plucked?

A metal bar when clamped at the centre, resonates in its fundamental frequency with longitudinal waves of frequency $4 \mathrm{kHz}$. If the clamp is moved to one end, what will be the fundamental resonance frequency?

A closed organ pipe $70 \mathrm{cm}$ long is sounded, If the velocity of the sound is $331 \mathrm{m}/\mathrm{s}$, what is fundamental frequency of vibration of the air column?

A vertical tube is made to stand in water so that the water level can be adjusted. A sound wave of frequency is sent into the top of the tube. If standing waves are produced at two successive water levels of. $20 \mathrm{cm}$  and $73 \mathrm{cm}$ what is the speed of sound waves in the air in the tube 

Two organ pipes of length $65 \mathrm{cm}$ and $70 \mathrm{cm}$ are sounded simultaneously. How many beats per second will be produced between the fundamental frequencies of the two pipes ?
(Velocity of sound in air $330 \mathrm{m}/\mathrm{s}$ )
 

A train sounds its whistle as it approaches and crosses a level crossing. An observer at the crossing measures a frequency of $219 \mathrm{Hz}$ as the train approaches and a frequency of $184 \mathrm{Hz}$ as it leaves. If the speed of sound is taken to be $340 \mathrm{m}/\mathrm{s}$, find the speed of the train and the frequency of its whistle.
 

Two trucks heading in opposite directions with speeds of $60 \mathrm{kmph}$  and $70 \mathrm{kmph}$ respectively, approach each other. The driver of the first truck sounds his horn of frequency  $400 \mathrm{Hz}$. What frequency does the driver of the second truck hear? (velocity of sound $330 \mathrm{m}/\mathrm{s}$) After the two trucks have passed each other,