Phase constant problem, two trumpets

[Daniiel]

Two trumpeters are standing 3m apart and blowing in the same not at 932Hz. A listener stands directly infront of one of the trumpeters. 10m from the wall. Take the velocity of sound to be 340m/s.

i) what is the phase difference between the two waves when they reach the listener?
ii)what frequency closest to 932Hz would produce a minimum intensity at the listener?

I think i have part i down
what i did was (making p = phase constant and w wave length, dl change in distance)

p=2dLpi/w
v=fw
so
p = (2pi dL f) / v
and i got 52.4

then for part ii I am not sure what to do, the equation for intensity involves power in my book
im not sure how to find power
thanks

 

[merryjman]

well, all you really need to do is think about phase difference. What would the phase difference be in order to produce minimum intensity? If you know that, then you can work backwards to find the required frequency, in a similar manner to how you used a given frequency to find phase difference at 932 Hz.

 

[Daniiel]

ohh
so would that be when the phase difference is like
180? pi?
thanks

 

[Daniiel]

or would it be like 90 degrees? pi/2

 

[rwisz]

For part i, your calculation of the phase difference is correct. The phase difference between the two waves will be 52.4 degrees.

For part ii, we can use the equation for intensity, which is given by: I = P/A, where P is the power and A is the area. We can assume that the power is constant for both trumpeters, so we just need to focus on the area.

Since the listener is standing 10m from the wall, we can consider the listener to be at the center of a circle with a radius of 10m. The two trumpeters are standing 3m apart, so the distance between them and the listener is also 10m. This creates a triangle with two sides of 10m and an angle of 52.4 degrees between them (since this is the phase difference between the two waves).

Using the law of cosines, we can find the third side of the triangle, which is the distance between the two trumpeters. Let's call this distance x.

x^2 = 10^2 + 10^2 - 2(10)(10)cos(52.4)
x^2 = 200 - 200cos(52.4)
x = 4.7m

Now, the area of a circle is given by A = πr^2, where r is the radius. In this case, the radius is the distance between the two trumpeters, which we just calculated to be 4.7m.

So, the area of the circle is A = π(4.7)^2 = 69.4m^2.

Now, we can plug these values into the equation for intensity to find the minimum intensity:

I = P/A = P/69.4m^2

To find the frequency that would produce this minimum intensity, we need to rearrange the equation for frequency:

f = v/wavelength

But we don't know the wavelength, so let's use the formula for wavelength in terms of frequency and velocity:

wavelength = v/f

Plugging this into the equation for intensity, we get:

I = P/(A*v^2/f^2)

Since we are looking for the frequency that would produce the minimum intensity, we want to minimize this equation. To do that, we need to maximize the denominator. So, we can rewrite the equation as:

I = P*f^2/(A*v^