Learning Object L04 Sound Waves

1. Grandmothers Birthday
Learning Object L04 (Sound Waves)
Lily Li
Physics 101 section 202 (L2J)

2. It’s your grandmothers birthday and you want to take her to a special
Spice Girls reunion concert, but she can only withstand a sound
intensity level of 120 dB before getting a headache. After talking to
the stage manager, you find out that the speakers radiate 10744.25
Watts (1.07x104
Watts) and that she would be fine as long as she
stood at least 30m away from the speakers.
A) What’s the sound intensity (I) at this distance (30m)?
B) You want to make sure that the stage manager has the numbers
right. Calculate the sound intensity level (dB). Is this distance safe
for your grandmother to enjoy the concert?

3. ANSWERS
A) Given the power (10744.25 Watts) and radius (30m), we can use the
equation 𝐼 =
𝑃
4𝜋𝑟2 to solve for the sound intensity…
𝐼 =
10744.25𝑊
4𝜋(30𝑚)2
= 0.95 W𝑚−2
B) Now that we have calculated the sound intensity, we can use it to
calculate the sound intensity level and check that it is under 120dB using
the equations 𝛽 = 0𝑑𝐵 + 10 log
𝐼
𝐼0
and 𝐼0 = 10−12 𝑊
𝑚2
𝛽 = 0𝑑𝐵 + 10 log
0.95
𝑊
𝑚2
10−12 𝑊
𝑚2
= 119.78dB (Yes it’s safe because 119.78dB < 120dB)