Calculating Frequency Shift for Temperature Change in Musical Instruments

[Gauss177]

Homework Statement

1. An unfingered guitar string is 0.70 m long and is tuned to play E above middle C (330 Hz). How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?

2. An organ is in tune at 20 degrees C. By what fraction will the frequency be off at 0 degrees C?

Homework Equations

The Attempt at a Solution

1. I used the v=(freq)(wavelength) equation:
v = (330)(0.70) = 231 m/s
Then i plugged in 231 to figure out the distance for 440 Hz:
(231 m/s) = (440)x
x=.525 m
I'm not sure if my method is right, so please check that! thanks

2. Not sure about this one

Thanks for the help

 

[chaoseverlasting]

I think that's right.

For the second part,
$$v=\sqrt{\frac{\gamma RT}{M}}$$ The temperature should be in Kelvin. Since there is no change in the gas, $$\frac{\gamma R}{M}$$ are constant, and so the speed of sound varies with the square root of temperature. That should help you out.