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Whistles in the Cold: Sound Waves on a Winter Camping Trip

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Whistles in the Cold: Sound Waves on a Winter Camping Trip

Use echoes, whistle tones and a snow shelter test to work with wavelength, amplitude and energy.

Part 1: Echoes and whistle tones

Read the trip notes and study Table 1. Then answer the questions.

Trip Notes: Signals in the Snow

1In February, the Timberline Outdoor Club spent two nights at a winter campsite beside a frozen lake. Club leader Mr. Gustavo Ilunga taught the group how to stay warm: wear layers, keep a dry hat on, and sleep in a quinzhee, a snow shelter made by piling up a large mound of snow and hollowing it out. Its thick snow walls hold in the campers' body heat. He also gave every camper an emergency whistle, because three sharp blasts are a common call for help. Sound is a mechanical wave. The whistle makes the air vibrate, and each bit of air passes the push and pull along to the next bit, while the air itself mostly moves back and forth in place.

2On the first morning, the air was −10 °C. Eighth grader Siobhan Mercado stood on the shore facing a rock cliff across a narrow arm of the lake. On the club's trail map, the cliff is 162.5 m from that spot. She gave one short blast on a whistle, and a sound app on her phone measured the time from the blast to its echo: 1.00 s in each of three tries. Mr. Ilunga said the club had done the same test from the same spot on its summer trip, when the air was 25 °C. That time the echo came back after 0.94 s.

3Next, Kenta Oberlin used the app to measure the frequency of three different whistles, the number of vibrations each second in hertz (Hz). Siobhan used her echo result and the rule wave speed = frequency × wavelength to work out each whistle's wavelength in the −10 °C air (Table 1).

4That afternoon, the campers wanted to know whether someone sleeping in the quinzhee would hear a whistle from outside. Siobhan set her phone 10 m from a marked spot, first in the open air, then inside a tent and then inside the quinzhee. Each time, Kenta stood on the marked spot and gave whistle B one hard blast, trying to blow the same way every time. The app showed the amplitude of the sound wave, how strongly the air was squeezed and stretched, and the sound energy reaching the phone, both in the app's own units. Last, Kenta gave one soft blast with the phone in the open air (Table 2). Mr. Ilunga explained that fresh snow soaks up much of the sound that hits it, which is why a quinzhee can feel so quiet inside.

Table 1: Whistle Tones in −10 °C Air
WhistleFrequency (Hz)Wavelength (m)
A32500.1
B2600?
C16250.2
1.
Use paragraph 2. The echo traveled from Siobhan to the cliff and back again.

The speed of sound in the −10 °C air was m/s.

2.
Use your answer to question 1 and wave speed = frequency × wavelength to find the missing value in Table 1. Do not round.

The wavelength of whistle B's sound in the −10 °C air is m.

3.
Compare whistles A and C in Table 1. Which statement fits the data?
Question 3 options
4.
Use paragraph 2. Suppose whistle A, still at 3,250 Hz, had been blown on the summer trip at 25 °C. How would the wavelength of its sound compare with the 0.10 m in Table 1?
Question 4 options

Part 2: The snow shelter test

Study Table 2 and use paragraph 4 to answer the questions.

Table 2: Whistle B Heard From 10 m Away
BlastWhere the phone wasAmplitude (units)Energy (units)
HardOpen air864
HardInside the tent636
HardInside the quinzhee3?
SoftOpen air416
5.
Compare the hard blast and the soft blast in the open air.

The hard blast had twice the amplitude of the soft blast, and it delivered times as much energy.

6.
The same amplitude–energy rule fits every complete row of Table 2. Use it to find the missing value.

The energy reaching the phone inside the quinzhee was units.

7.
Inside the tent, the amplitude of the hard blast was 3/4 of its amplitude in the open air. What fraction of the open-air energy reached the phone inside the tent?
Question 7 options
8.
The campers want a whistle blast from the marked spot to deliver 36 units inside the quinzhee, as much as the hard blast delivered inside the tent. Suppose the quinzhee walls always cut the amplitude to the same fraction as in Table 2. How much energy would that blast need to deliver in the open air at 10 m?
Question 8 options
9.
Use the trip notes and both tables. Sort each change by the property of the sound wave it changes most directly.
10.
Kenta says, "The quinzhee cut the amplitude from 8 units to 3 units, so about 3/8 of the whistle's energy still got inside. That's more than a third, so a sleeper will hear it fine." Do you agree with his math? Write a claim, give evidence from Table 2, and explain your reasoning about how a wave's amplitude is related to the energy it carries.