What is the speed of an earthquake S-wave with a 2.3 X10^4 m wavelength and a 0.065 Hz frequency?

Answer 1

Frequency (1/s or Hz) = speed (m/s) / wavelength (m)

So we can solve for the speed

Speed = wavelength * frequency

Speed = 2.3*10^4 m * 0.065 (1/s) = 1495 m/s = 1.5*10^3 m/s (2 sig figs)

Answer 2

The speed of a wave will be found by multiplying the wavelength by the frequency. In this case, 2.3x10^4 meters times 0.065 Hz (or 1/s) will yield a wave speed of 1.495x10^3 m/s.

This frequency can be thought of as the number of wavelengths that pass by a point in one unit of time, one second in this case. Therefore, knowing the length of one wave, we can multiply that wavelength by the number of waves that pass by in a certain amount of time to find the speed at which that wave is moving.

If you don't know this relationship off of the top of your head, or can't recall it in the future, I would recommend paying close attention to the units of the given values and the units of what you are trying to find. Speed has units of length/time. Wavelength has units of length. Frequency has units of 1/time. To calculate a speed, you need to find an operation that will yield length/time using length and 1/time. If you multiply these two units, you will achieve the desired units for speed, and thus you will have found the speed of the wave.

Cheers!

Justin