1. (JEE Main 2022 (Online) 24th June Evening Shift)

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 $y = (10 \cos π x \sin \frac{2 π t}{T})$ cm

The amplitude of the particle at $x = \frac{4}{3}$ cm will be ___________ cm.

Correct Answer is 5

$A = | 10 \cos (π x) |$

At $x = \frac{4}{3}$

$A = | 10 \cos (π \times \frac{4}{3}) |$

$=$ | $-$ 5 cm |

$∴$ Amp = 5 cm

2. (JEE Main 2021 (Online) 26th August Morning Shift)

Two travelling waves produces a standing wave represented by equation,

y = 1.0 mm cos(1.57 cm^{$-$ 1}) x sin(78.5 s^{$-$ 1})t.

The node closest to the origin in the region x > 0 will be at x = .............. cm.

Correct Answer is 1

For node

cos(1.57 cm^{$-$ 1})x = 0

(1.57 cm^{$-$ 1})x = $\frac{π}{2}$

x = $\frac{π}{2 (1.57)}$ cm = 1 cm

3. (JEE Main 2017 (Online) 9th April Morning Slot)

A standing wave is formed by the superposition of two waves travelling in opposite directions. The transverse displacement is given by

y(x, t) = 0.5 sin $(\frac{5 π}{4} x)$ cos(200 $π$ t).

What is the speed of the travelling wave moving in the positive x direction ?

(x and t are in meter and second, respectively.)

A. 160 m/s

B. 90 m/s

C. 180 m/s

D. 120 m/s

Correct Answer is Option (A)

Standard equation of standing wave,

y(x, t) = 2a sin kx cos $ω$ t

Given,

y(x, t) = 0.5 sin $(\frac{5 π}{4} x)$ cos (200 $π$ t).

So, k = $\frac{5 π}{4}$ and $ω$ = 200 $π$

$∴$ Speed of travelling wave

= $\frac{ω}{k}$ = $\frac{200 π}{\frac{5 π}{4}}$ = 160 m/s.

4. (AIEEE 2002)

length of a string tied to two rigid supports is $40$ $c m$ . Maximum length (wavelength in $c m$ ) of a stationary wave produced on it is :

A. 20

B. 80

C. 40

D. 120

Correct Answer is Option (B)

This will happen for fundamental mode of vibration as shown in the figure. $S_{1}$ and $S_{2}$ are rigid support

Here $\frac{λ}{2} = 40$ $∴$ $λ = 80 c m$

AIEEE 2002 Physics - Waves Question 125 English Explanation