Two waves traveling on a string in the same direction both have a frequency of 135 Hz, a wavelength of 2 cm, and an amplitude of 0.04 m. What is the amplitude of the resultant w…

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asked Apr 28, 2020 222k views

1 Answer

Muki · Answer 1 · 2020-05-02T09:12:45+0000

Answer:

The amplitude of the resultant wave are

(a). 0.0772 m

(b). 0.0692 m

Step-by-step explanation:

Given that,

Frequency = 135 Hz

Wavelength = 2 cm

Amplitude = 0.04 m

We need to calculate the angular frequency

$\omega=2\pi f$

$\omega=2*\pi*135$

$\omega=848.23\ rad/s$

As the two waves are identical except in their phase,

The amplitude of the resultant wave is given by

$y+y=A\sin(kx-\omega t)+Asin(kx-\omega t+\phi)$

$y+y=A[2\sin(kx-\omega t+(\phi)/(2))\cos\phi(\phi)/(2)$

$y'=2A\cos((\phi)/(2))\sin(kx-\omega t+(\phi)/(2))$

(a). We need to calculate the amplitude of the resultant wave

For
$\phi =(\pi)/(6)$

The amplitude of the resultant wave is

$A'=2A\cos((\phi)/(2))$

Put the value into the formula

$A'=2*0.04\cos((\pi)/(12))$

$A'=0.0772\ m$

(b), We need to calculate the amplitude of the resultant wave

For
$\phi =(\pi)/(3)$

$A'=2*0.04\cos((\pi)/(6))$

$A'=0.0692\ m$

Hence, The amplitude of the resultant wave are

(a). 0.0772 m

(b). 0.0692 m