Question

A transverse, sinusoidal wave travels in a string and can be described by the function: y(x,t)=0.87 sin(21x−4.9t). What is the speed of this wave?A transverse, sinusoidal wave travels in a string and can be described by the function: . What is the speed of this wave?

A. 0.18 m/s
B. 9.2 m/s
C. 4.3 m/s
D. 0.23 m/s

Answer 1

D. 0.23m/s

Step-by-step explanation:

Given the equation of a wave expressed as;

y(x,t)=0.87 sin(21x−4.9t)

Comparing with the standard equation of a wave;

y(x,t)= Asin(2πx/λ−2πft) where;

f is the frequency

λ is the wavelength

On comparing;

2πx/λ = 21x

2π/λ = 21

λ = 2π/21

λ = 2(3.14)/21

λ = 6.28/21

λ = 0.299m

Get the frequency f;

2πft = 4.9t

2πf = 4.9

f = 4.9/2π

f = 4.9/2(3.14)

f = 4.9/6.28

f = 0.78Hz

Get the speed of the wave

Speed = frequency * wavelength

Speed = 0.299 * 0.78

Speed = 0.233m/s

Hence the speed of the wave is 0.23m/s