Transverse wave problem. It's a doozy

[Mr. Sinister]

Transverse wave problem... It's a doozy!

Homework Statement

A certain transverse wave is described by the equation,
y(x,t)=(2 m) sin[(174.5 s -1)t - (22.44 m-1) x]. What is the frequency,wave's period, wavelength, and wave speed?

Homework Equations

v=wavelength * f= wavelength/T

The Attempt at a Solution

I believe that 174.5 is the frequency. That is all that I know that could be correct. Could somebody please throw some more equations my way and possibly give me some hints. Thanks.

 

[BishopUser]

174.5 is more likely to be an angular frequency... you should be able to relate that to regular frequency and period quite easily. your relevant equations should take care of the rest

 

[ogb p]

I would approach this problem by first identifying the given variables and their units. In this case, we have y (position, in meters), x (position, in meters), t (time, in seconds), frequency (in hertz), wavelength (in meters), and wave speed (in meters per second).

Next, I would look at the given equation and try to identify any patterns or relationships between the variables. In this case, we can see that the wave is sinusoidal, with a maximum amplitude of 2 meters. The frequency, given by the coefficient in front of t, is 174.5 s^-1. This means that the wave oscillates 174.5 times per second.

We can also see that the coefficient in front of x, 22.44 m^-1, represents the wavelength. This means that the distance between two consecutive peaks or troughs of the wave is 22.44 meters.

Using the equations v = fλ and T = 1/f, we can find the wavelength and period of the wave. The wavelength is simply 22.44 meters, and the period is 1/174.5 s^-1, which is approximately 0.0057 seconds.

To find the wave speed, we can use the equation v = λf. Substituting in our values for wavelength and frequency, we get v = (22.44 m)(174.5 s^-1) = 3915.3 m/s.

In summary, the frequency of the wave is 174.5 Hz, the period is approximately 0.0057 seconds, the wavelength is 22.44 meters, and the wave speed is 3915.3 m/s. I hope this helps!