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Chapter 14: Problem 9

The speed of sound in air at \(27^{\circ} \mathrm{C}\) is \(340 \mathrm{~m} / \mathrm{s}\) in rainy season, it is found that sound travels \(660 \mathrm{~m}\) in two second in a given season. Assume that no variation takes place in density of air due to variation of season. The season on the basis of temperature is: (a) winter (b) summer (c) may be summer or winter (d) all of the above

Short Answer

Expert verified
The season based on temperature is winter (option a).

Step by step solution

01

Calculate the Speed of Sound

The problem states that the sound travels 660 m in 2 seconds during the given season. Therefore, we use the formula for speed, which is \( \text{speed} = \frac{\text{distance}}{\text{time}} \). Plugging in the values, we get: \[ \text{speed} = \frac{660}{2} = 330\, \text{m/s} \] This speed is specific to the unknown season we are trying to determine.
02

Compare Seasonal Speeds

We are given that the speed of sound at 27掳C is 340 m/s. We can infer temperature affecting seasons as follows: colder temperatures (winter) would decrease the speed of sound, while warmer temperatures (summer) would increase it. Given a speed of 330 m/s, which is less than 340 m/s, we can deduce the season as winter due to the lower speed correlating with a lower temperature.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Temperature and Sound Speed
The speed of sound in air is influenced significantly by temperature. As a rule of thumb, the hotter the temperature, the faster sound travels. This is because molecules at higher temperatures have more energy, allowing sound waves to pass through them more quickly.

When a sound wave travels through the air, it essentially transfers energy from one molecule to another. In cold conditions, the molecules are less energetic and move more slowly, which results in a slower transfer and thus a lower speed of sound.

It is useful to remember the general relationship: for every 1掳C increase in temperature, the speed of sound increases by approximately 0.6 m/s. Therefore, temperature variations throughout the year can cause noticeable changes in the speed of sound.
Seasonal Effects on Sound
Different seasons can lead to variations in the speed at which sound travels in the air. This is because each season often has a typical range of temperatures.

During winter, temperatures are generally lower, and as a result, the speed of sound decreases. Conversely, in summer, with higher ambient temperatures, the speed of sound increases. Spring and autumn might show intermediate values depending on specific weather conditions.

In the exercise, the speed is calculated to be 330 m/s, which is slower than the speed given for 27掳C at 340 m/s. Since lower speeds are associated with colder temperatures, we can infer that the season in question is likely winter.
Thermal Physics Concepts
Thermal physics principles help us understand how temperature affects various physical properties. In this context, it impacts the speed of sound in air.

The kinetic theory of gases provides insight into this relationship. It postulates that gases consist of rapidly moving particles. When the temperature increases, energy in these particles increases, and they move more rapidly. Consequently, sound鈥� being a mechanical wave relying on particle interaction鈥� travels more quickly.

Similarly, in colder temperatures, particles move less vigorously, decreasing the speed of sound. Thus, using thermal physics, we can correlate changes in temperature with changes in sound speed and apply this understanding to predict seasonal variations in sound behavior.

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Most popular questions from this chapter

An air column in a pipe which is closed at one end will be in resonance with a vibrating tuning fork of frequency \(264 \mathrm{~Hz}\) if the length of the air column in \(\mathrm{cm}\) is: (Speed of sound in air \(=340 \mathrm{~m} / \mathrm{s}\) ) (a) \(32.19 \mathrm{~cm}\) (b) \(64.39 \mathrm{~cm}\) (c) \(100 \mathrm{~cm}\) (d) \(140 \mathrm{~cm}\)

Two sources \(A\) and \(B\) are sounding notes of frequency \(680 \mathrm{~Hz}\). A listener moves from \(A\) to \(B\) with a constant velocity \(u\). If the speed of sound is \(340 \mathrm{~m} / \mathrm{s}\), what must be the value of \(u\), so that he hears 10 beats per second? (a) \(2 \mathrm{~m} / \mathrm{s}\) (b) \(2.5 \mathrm{~m} / \mathrm{s}\) (c) \(3 \mathrm{~m} / \mathrm{s}\) (d) \(3.5 \mathrm{~m} / \mathrm{s}\)

A boy is sitting on a swing and blowing a whistle at a frequency of \(1000 \mathrm{~Hz}\). The swing is moving to an angle of \(30^{\circ}\) from vertical. The boy is at \(2 \mathrm{~m}\) from the point of support of swing and a girl stands infront of swing. Then the maximum frequency she will hear, is : (Given: velocity of sound \(=330 \mathrm{~m} / \mathrm{s}\) ) (a) \(1000 \mathrm{~Hz}\) (b) \(1001 \mathrm{~Hz}\) (c) \(1007 \mathrm{~Hz}\) (d) \(1011 \mathrm{~Hz}\)

An organ pipe closed at one end resonates with a tuning fork of frequencies \(180 \mathrm{~Hz}\) and \(300 \mathrm{~Hz}\). It will also resonate with tuning fork of frequencies: (a) \(360 \mathrm{~Hz}\) (b) \(420 \mathrm{~Hz}\) (c) \(480 \mathrm{~Hz}\) (d) \(540 \mathrm{~Hz}\)

From a height of \(2 \mathrm{~m}\), a drop of water of radius \(2 \times 10^{-3} \mathrm{~m}\) fall and produces a sound. The sound produced can be heard upto a distance of 20 metre. If the gravitational energy is converted into sound energy in \(0.5 \mathrm{~s}\), then the intensity at a distance of \(20 \mathrm{~m}\) is : (a) \(2 \times 10^{-7} \mathrm{~W} / \mathrm{m}^{2}\) (b) \(2.6 \times 10^{-6} \mathrm{~W} / \mathrm{m}^{2}\) (c) \(2.6 \times 10^{-7} \mathrm{~W} / \mathrm{m}^{2}\) (d) \(3 \times 10^{-7} \mathrm{~W} / \mathrm{m}^{2}\)
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