Two travelling sinusoidal waves are described by the wave functions y1=10sin[pi(8x−1400t)] and y2=10sin[pi(8x−1400t−0.5)] Where x, y1, and y2 are in metres and t is in seconds . which of the following options is/are correct ? Amplitude of the resultant wave is 10sqrt(2) m Frequency of the resultant wave is 700 Hz Time period of the resultant wave is 0.1 s None of these

Taliyah Esparza

Taliyah Esparza

Answered question

2023-01-07

Two travelling sinusoidal waves are described by the wave functions y1=10sin[pi(8x−1400t)] and y2=10sin[pi(8x−1400t−0.5)] Where x, y1, and y2 are in metres and t is in seconds . which of the following options is/are correct ?
Amplitude of the resultant wave is 10sqrt(2) m
Frequency of the resultant wave is 700 Hz
Time period of the resultant wave is 0.1 s
None of these

Answer & Explanation

Ezekiel Robbins

Ezekiel Robbins

Beginner2023-01-08Added 8 answers

y = A sin ( k x ω t + ϕ ) y = y 1 + y 2 y r = y 1 + y 2 y r = 2 A 0 cos ( ϕ 2 ) sin ( k x ω t ϕ 2 ) y r = ( 2 × 10 ) cos ( π 4 ) sin [ π ( 8 x 1400 t ) π 4 ] y r = 10 2 sin [ π ( 8 x 1400 t ) π 4 ] A r = 10 2 ,   ω r = 1400 π f = 1400 π 2 π = 700 H z Time period (T) = 1 f = 1 700 = 0.0014   s e c
Answers is Amplitude of the resultant wave is 10sqrt(2) m and Frequency of the resultant wave is 700 Hz

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