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?

2.61m/s

Explanation:

Given the wave function;

y(x,t)=0.87 sin(21x−4.9t).

The general wave equation is expressed as;

f is the frequency of the wave

t is the time

is the wavelength

On comparing;

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 wavelength;

2πx/ = 21x

2π/ = 21

2π = 21

= 21/2π

= 21/2(3.14)

= 21/6.28

= 3.34m

Speed = frequency * wavelength

Speed of the wave = 0.78 * 3.34

Speed of the wave = 2.61m/s

Hence the speed of the wave is 2.61m/s

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