The document describes an experiment where a sister listens to different tones in each earbud. The right earbud plays a 500Hz tone and the left plays a 503Hz tone, creating a 3Hz beat frequency. It is expected that she will raise her hand every 3.33 seconds as she hears 10 beats. If the right tone increases to 501Hz, the beat frequency decreases to 2Hz. As a result, the time between each hand raise is expected to increase to 5 seconds.

1. Put your hand up
Learning Object L08 (Beats)
Lily Li
Physics 101 section 202 (L2J)

2. You want to test out beat frequencies so you ask your sister to put in
earbuds. The right earbud connected to an iPod playing a tone with a
frequency of 500Hz and the left earbud connected to an iPod playing
a tone with a frequency of 503Hz. You ask her to put her hand up for
every 10 beats she hears.
A) How many seconds do you expect between each time she puts up
her hand? (Neglecting timing/human errors between hand raises)
B) You increases the frequency of the right earbud by 1Hz, will the
time taken between each hand raise increase or decrease?

3. ANSWER
A) By taking the difference between the two frequencies (503 and 500), we
can determine the frequency of the beat, and find that she should hear
3 beats every second.
To find out how many times you should expect her to put her hand up:
10 𝑏𝑒𝑎𝑡𝑠
1 ℎ𝑎𝑛𝑑 𝑟𝑎𝑖𝑠𝑒
×
1 𝑠𝑒𝑐𝑜𝑛𝑑
3 𝑏𝑒𝑎𝑡𝑠
= 3.33 𝑠𝑒𝑐𝑜𝑛𝑑𝑠 𝑝𝑒𝑟 ℎ𝑎𝑛𝑑 𝑟𝑎𝑖𝑠𝑒
B) New frequency of the right earbud: 501Hz. Difference between
frequencies: 503-501 = 2 Hz. She will now hear 2 beats per second.
Repeating the procedure from part A:
10 𝑏𝑒𝑎𝑡𝑠
𝑠𝑒𝑐𝑜𝑛𝑑
×
1 𝑠𝑒𝑐𝑜𝑛𝑑
2 𝑏𝑒𝑎𝑡𝑠
= 5 𝑠𝑒𝑐𝑜𝑛𝑑𝑠 𝑝𝑒𝑟 ℎ𝑎𝑛𝑑 𝑟𝑎𝑖𝑠𝑒
5 seconds > 3.33 seconds, therefore by increasing the frequency in the
right earbud (and decreasing the difference between the frequencies), the
time taken between frequencies should also decrease.