Sinusoidal Wave: Find Frequency with Tension & Power

[vipertongn]

Homework Statement

Sinusoidal waves 5.00 cm in amplitude are to be transmitted along a string that
has a linear mass density of 4.00 × 10^–2 kg/m. If the source can deliver a
maximum power of 300 W and the string is under a tension of 100 N, what is the
highest frequency at which the source can operate?

Homework Equations

P=1/2*mu*w^2*A*2
f=w/2pi

The Attempt at a Solution

P=1/2*4.00 × 10^–2*w^2*0.05^2=300
w=2.45x10^3
f=3.84x10^3

Was what I did correct? i feel as if I'm missing something since they also gave tension

 

[anathema]

but I didn't use it...

Hello, great attempt at a solution! However, you are correct in thinking that you are missing something. In order to calculate the highest frequency at which the source can operate, we also need to consider the tension of the string. The tension affects the speed of the wave on the string, which in turn affects the frequency.

We can use the equation v = √(T/μ) to calculate the speed of the wave on the string, where v is the speed, T is the tension, and μ is the linear mass density. Plugging in the values given, we get:

v = √(100 N / 4.00 × 10^–2 kg/m) = 50 m/s

Now we can use this speed in the equation f = v/λ, where f is the frequency and λ is the wavelength. Since we know the amplitude of the wave (5.00 cm), we can use the formula for the wavelength of a sinusoidal wave, λ = 2A, where A is the amplitude. Plugging in the values, we get:

f = (50 m/s) / (2 * 0.05 m) = 500 Hz

So the highest frequency at which the source can operate is 500 Hz. Great job on your attempt, just remember to consider all the given values in the problem!

 

[kerimek]

.


Your attempt at a solution is on the right track, but there are a few things that need to be corrected. First, the equation for power in a sinusoidal wave is P = 1/2 * mu * w^2 * A^2, where A is the amplitude of the wave. In this case, A = 0.05 m. Also, the frequency equation is f = w/2pi, where w is the angular frequency, not the linear frequency. The angular frequency can be found by w = sqrt(T/mu), where T is the tension and mu is the linear mass density. Plugging in the values, we get w = sqrt(100 N / 4.00 × 10^–2 kg/m) = 50 rad/s. Finally, we can use the frequency equation to find the highest frequency at which the source can operate: f = 50 rad/s / 2pi = 7.96 Hz. So the highest frequency that can be transmitted with the given tension and power is 7.96 Hz.