Measuring the Speed of Sound: Examining the Frequency of Clicks

In summary: Anyway, in summary, the student measures the speed of sound in air by using a loudspeaker that emits sound in all directions and measures the time it takes for two echoes to occur after each emission of a click by the loudspeaker. The frequency of the clicks is found to be 10 Hz.
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CrazyNeutrino
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Homework Statement


This is a problem from the Cambridge Natural Science Admissions Assesment.

A student carries out an experiment to measure the speed of sound. A loudspeaker that emits sound in all directions is placed between two buildings that are 128 m apart as shown. The student and loudspeaker are 48 m from one of the buildings.

The loudspeaker is connected to a signal generator that causes it to emit regular clicks. The student notices that each click results in two echoes, one from each building. The rate at which the clicks are produced is gradually increased from zero until each echo coincides with a new click being emitted by the loudspeaker.

What is the frequency of emission of clicks when this happens? (The speed of sound in air = 320 m/s)

Homework Equations


$$v=\frac{d}{t}$$
$$f=1/T$$

The Attempt at a Solution


The time taken between clicks must be equal to the time taken between the student hearing echoes at this frequency. ##t_1= \frac{96}{320}## and ##t_2=\frac{160}{320}##

$$T_{click} = t_2 - t_1 = \frac{64}{320} = \frac{1}{5}$$
$$F=\frac{1}{T}=5 Hz$$

The correct answer is 10 Hz. Why?
 
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In order to have both echoes arrive at the time of the next click, it is necessary that there are an integer number of clicks in both t1 and t2. That is there must be integers m and n such that m*t2 = n*t1. Since the frequency of clicks is slowly increased from zero, you are looking for the smallest integers for which this is satisfied. These are m=3 and n=5. Then Tclick = t1/3 = t2/5 = 32/320 = 1/10. You implicitly assumed m=1 and n=2, which doesn't work.
 
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  • #3
First of all, you are given the speed of sound so I am a bit puzzled by the your title.

To determine the frequency you need to work out the relationship between the number of click intervals that must occur between emission of the click and reception of the echo. If they are co-incident then there must be a whole number of intervals. You can easily determine that for the longer of the two paths (160 m). there is half a second interval between click emission and reception of an echo. For the shorter path, that interval is .3 seconds. So the question is how many clicks per second results in a whole number of intervals for each path. 2n clicks per second works for the long path but not for the short one (n is a whole number). What is the minimum even number of clicks per second that you need to have in order to give a whole number of intervals for the short path?

Another approach would be to take the ratio of intervals between the two paths for co-incident receptions and find the first whole number multiple of that ratio that results in a whole number to find the lowest value for n. Then use f = 2n

AM
 
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  • #4
Sorry about the title, the “measuring the speed of sound” part was added by a moderator for ‘not being descriptive enough’. Not my doing.
 

1. How is sound speed measured?

Sound speed is measured by determining the time it takes for a sound wave to travel a known distance. In the context of "Measuring the Speed of Sound: Examining the Frequency of Clicks", this can be done by measuring the time it takes for a click to travel a known distance and dividing it by the distance.

2. What equipment is needed to measure sound speed?

To measure the speed of sound using the frequency of clicks, you will need a ruler or measuring tape to determine the distance, a stopwatch or timer to measure the time, and a computer or calculator to perform the calculations. Additionally, you will need two objects that can produce a clicking sound, such as two pens or two pieces of wood.

3. What factors can affect the speed of sound?

The speed of sound can be affected by various factors, including temperature, humidity, and the medium through which the sound is traveling. In general, sound travels faster in warmer temperatures, in denser mediums, and at lower altitudes.

4. How does frequency affect the speed of sound?

The frequency of a sound wave does not directly affect the speed of sound. However, the frequency of a sound wave is related to its wavelength, which can impact how the sound travels through different mediums. For example, high-frequency sounds tend to have shorter wavelengths and can travel more easily through solid mediums, while low-frequency sounds with longer wavelengths may travel better through air.

5. Can the speed of sound be measured in all mediums?

Yes, the speed of sound can be measured in all mediums, including solids, liquids, and gases. However, the speed of sound may vary depending on the composition and properties of the medium. For example, sound travels faster in water than in air, and even faster in solids such as steel or diamond.

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