Question

FIGURE EX17.7 shows a standing wave on a string that is oscillating at 100 Hz. a. How many antinodes will there be if the frequency is increased to 200 Hz? b. If the tension is increased by a factor of 4, at what frequency will the string continue to oscillate as a standing wave that looks like the one in the figure?

Short answer

a) 8

b) 200Hz

Step-by-step solution

Given information

A wave is oscillating with frequency 100Hz on a string fixed at both ends.

Part a:

Antinodes are inversely proportional to wavelength. So if we double the frequency, wavelength will be halved and so therefore antinodes will be doubled. i.e. $4\times 2=8$antinodes.

Part b:

We know that frequency is directly proportional to square root of tension.

So if we increase tension by 4 times, frequency has to be doubled i.e. $100Hz\times 2=200Hz$ to keep the wave oscillating as it was initially.