# Sound problems

1. Nov 17, 2005

### dustybray

These questions are giving me some trouble:

6. A loudspeaker at a rock concert generates 1 x 10^-2 W/m^2 at 20 m at a frequency of 1.0 kHz. Assume the speaker spreads its energy uniformly in all directions.

a. What is the intensity level in dB at 20 m?
b. What is the total acoustic power output of the speaker?
c. At what distance from the speaker will the intensity level be at the pain threshold of 120 dB?
d. What is the intensity level in dB at a distance of 100 m from the speaker?

I don't understand how frequency affects intensity.

Should I use something other than these formulas?:

P = I * 4πr^2

β = 10 * log( I / 1*10^-12 W/m^2 )

2. A violin string is 30cm long between its fixed ends and has a mass of 2.0g. The open string (no finger applied) sounds an A note (440 Hz).

a. Calculate the tension in the string.

f[1] = v / 2L

v = f[1] * 2L

v = (440 Hz) * ( 2 * .3m ) = 264m/s

µ = M / L = .002kg / .3m = .0067kg/m

v = sqrt( F / µ )

F = µv^2

F = (.0067kg/m) (264m/s)^2 = 467N

b. What tension would be required for this open string to sound a C note (528 Hz)?

F = µv^2

Not sure how to approach this…

c. If instead of changing the tension you decide to sound a C note by stopping the string (pressing it against the violin with your finger), how far from the end of the string should it be applied?

L = v / 2f

L = 264m/s / ( 2 * 528Hz ) = .25m

Δx = L[0] – L = .3m - .25m = .05m