Calculating Wave Properties: Frequency, Wavelength, and Speed

[anotherperson]

Homework Statement

the displacement of a wave traveling in the negative x-direction is given by
y(x,t)=(5.2cm)cos(5.5x/m+72t/s)

where x is in metres, t is in seconds, calculate:
i)the frequency
ii) the wavelength
iii) the speed of this wave)

The Attempt at a Solution

i have absolutely no idea how do calculate the first 2. i thought you could just read the frequency and wavelength of the equation but this doesn't match my solutions

i know part iii) will be speed=72/5.5= 13 m/s

 

[Apophilius]

Remember that the equation of a wave is y(x,t) = ymsin(kx +- wt). In this case its s(x,t) = smcos(kx +- wt). Your equation above takes the form of the latter. Frequency is related to w by the equation w = 2pi f where f is frequency - so just plug in the w from your equation and solve. Also, k is related to wavelength (I'll label wavelength as y) by the equation k = (2pi)/y. Here you also just need to plug in your values from the equation and solve. And yeah, you're right about the speed. v = w/k.

 

[anotherperson]

this is exactly what i had done but i had used k for w and w for k, that's for the help!

 

[anotherperson]

thanks**

 

[rwisz]

I can help you understand how to calculate the frequency and wavelength from the given equation. The frequency of a wave is the number of complete oscillations it makes in one second. In this case, we can determine the frequency by looking at the coefficient in front of the time variable, which is 72/s. This means that the wave completes 72 oscillations in one second, giving us a frequency of 72 Hz.

The wavelength of a wave is the distance between two consecutive points of the same phase (e.g. two consecutive crests or troughs). In this equation, the wavelength is represented by the value inside the cosine function, which is 5.5x/m. This means that the wavelength is 5.5 meters.

Now, to calculate the speed of the wave, we can use the formula v = fλ, where v is the speed, f is the frequency, and λ is the wavelength. Substituting the values we calculated, we get v = (72 Hz) x (5.5 m) = 396 m/s. Therefore, the speed of this wave is 396 m/s.

I hope this helps you understand how to calculate the frequency, wavelength, and speed of a wave. Keep up the good work with your homework!