Problem 8P

Consider a wave on a string with constant tension. If the frequency of the wave is doubled, by what multiplicative factor does (a) the speed and (b) the wavelength change?

Solution 8P

a.)

Step 1 of 2

We have to find by what multiplicative factor does the speed of a wave on a string with constant tension changes when its frequency is doubled.

The speed of a wave on a string is given by the expression,

where,

Tension in the string in N

mass per unit length kg/m

Now, since the speed of a wave on a string is independent of the frequency and tension and mass per unit length being constant. The speed will remain the same even if the frequency is doubled.

Therefore, the speed of a wave on a string remains unchanged or changes by a multiplicative factor of 1.

b.)