Physics of Music PHY103 Worksheet #1 Set up for Lab #1

Physics of Music PHY103 Worksheet #1
Set up for Lab #1
1) Definition of frequency and period. A sine wave can be described by the
function f ( t) = Asin( ωt) = Asin(2 π ft)
of time t. Here A is the amplitude, ω is
the angular frequency and f is the frequency. The frequency, f, is given in units of
Hertz (Hz) or cycles/second (same thing) when the time, t, is in seconds. The
angular frequency is in units of radians per second. There are 2π radians or 360
degrees in a circle. Remember that sin(0) = 0 , sin( π / 2) = 1 , sin( π ) = 0 ,
sin(3 π / 2) = −1and sin(2 π ) = 0 .
Period
a) What is the frequency in Hz of the sine wave shown above?
b) What is the period in seconds of the sine wave?
c) What is the amplitude of the sine wave?
d) What would be the formula f(t) for a sine function that has twice the amplitude of
the above wave and a frequency of 1000 Hz?

2) Accuracy
a) Suppose you have a counter that measures frequency in Hz. It only measures
integer values. Suppose you have a signal that is 300Hz. Since it only measures Hz
in integer values the measurement would have an error of at least 1 Hz or a fractional
error of 1/300=0.0033 or 0.33%. What fractional error would you get if you measured
a 10Hz signal? A 100kHz signal?
b) Suppose you measure frequency on the oscilloscope and you adjust the time axis
so that 1 period of the signal covers 2 boxes on the scope. The error in measurement
you estimate from the screen by eye would be approximately 1/5 box or 1/10 of a
period. How accurately can you measure the frequency of a 10kHz signal? How
accurately can you measure the frequency of a 1kHz signal?
3) Practicing unit conversion.
Suppose I want to convert 6 inches into cm. 1 inch = 2.54cm. I can remember that
cm are smaller and so I want a bigger number. This means that I multiply by 2.54.
2.54 cm
Or I could write the problem like this 6 inches × = 15.24cm . Note that the
inches
inches cancel on the left hand side in this operation. If I write the problem this way
then I don’t need to think too hard about whether to divide or multiply by 2.54.
inches
Suppose I want to convert 10 cm into inches. 10cm × = 3.94inches . Note the
2.54 cm
cm cancel in the operation.
a) The speed of sound is approximately 742 miles/hour. Convert this into metric units
of cm/s. Hint (This requires converting the miles into inches and the inches into cm.
The hours must be converted to minutes and the minutes into seconds.) 1 mile is
equivalent to 63 360 inches.