Two sinusoidal waves and of equal amplitude travel along the same stretched string in…

PHYSICS · Subjective · CBSE · Physics · Waves · Waves

Problem

Two sinusoidal waves

A

and

B

of equal amplitude travel along the same stretched string in the same direction. At the fixed point

x = 0

, their displacement–time traces have the following properties: • Wave

A

has a period of

4.0\,\text{ms}

; at

t = 0

its displacement is zero and increasing positively. • Wave

B

has a period of

4.2\,\text{ms}

; at

t = 0

its displacement is zero and also increasing positively. At

t = 0

, a separate displacement–position snapshot of wave

A

shows successive crests that are

1.36\,\text{m}

apart. Using these data, answer the questions below. (a) Find the frequencies of waves

A

and

B

. (b) Determine the wavelength of wave

A

and hence the common speed of the two waves along the string. (c) Calculate the beat frequency produced at

x = 0

when the two waves superpose. (d) After what minimum time after

t = 0

will the resultant amplitude at

x = 0

again attain its maximum value?