Need help with physics Homework

Question

1) A water wave passes a boat every 32 seconds. What is the frequency of the waves in Hz?

 

 

2)A set of waves has a frequency of 39 Hz and a speed of 5 m/s. What is the wavelength of the waves in meters?

 

 

3)The frequency of an electromagnetic wave is 38316 Hz. What is the wavelength of the light in meters? 

Answer 1

Hi Juan,

 

1) Water waves are a periodic phenomenon, meaning that they repeat themselves over and over again in a given time period. The frequency is how many of these wave forms pass a point in a given time. The SI unit of frequency is the Hertz, abbreviated Hz, and it stands for "per second" or s^-1. If a boat passes once every 32 seconds, then f = 1/32s  = 1/32 Hz.

 

2) A special relationship always holds for waves. It is speed = wavelength X frequency, or in symbols v = λf. We want to find λ, so we solve for it:

 

λ = v/f = (5 m/s) / (39 Hz) = 0.128 Hz

 

3) This problem is in the same form as #2 above, except that we must know that electromagnetic waves travel at a special speed, the speed of light c = 3.0 X 10⁸ m/s. We are told that f = 38316 Hz. So, we solve for the wavelength as we did in #2 to get:

 

λ = v/f = = (3.0 X 10⁸ m/s) / (38316 Hz) = 7830 m

 

 

Answer 2

(1)

 

T = period = 32 s

 

f = frequency = 1/T = 1/32 s^-1 = 0.03125 Hz (same as cycles per second)

 

(2)

 

v = λf ⇒ λ = v/f = (5 m/s) / (39 Hz) ≅ 0.1282 m

 

(3)

 

λ = c/f = (3 x 10⁸ m/s) / (38316 Hz) ≅ 7830 m

 

The given frequency seems extremely low for light, resulting in an extremely high and unrealistic wavelength.  Could you double-check that frequency?