Chapter 16: Q. 5 (page 450)

Rank in order, from largest to smallest, the wavelengths $λ_{a}, λ_{b} a n d λ_{c}$ for sound waves having frequencies $f_{a} = 100 H z, f_{b} = 1000 H z, a n d f_{c} = 10, 000 H z$ . Explain.

Short Answer

Expert verified

The largest wavelength is $λ_{a}$ and the smallest wavelength is $λ_{c}$ .

$λ_{a} > λ_{b} > λ_{c}$

Step by step solution

Step 1. Write the given information.

The wavelengths of the sound wave are given by $λ_{a}, λ_{b} a n d λ_{c}$
The frequency of waves is role="math" localid="1648816875381" $f_{a} = 100 H z, f_{b} = 1000 H z, a n d f_{c} = 10, 000 H z$
respectively.

The speed of the wave is given by the formula $λ f = c$
Here, c is the speed of light (3x10⁸m/s²) which is constant.

Step 2. To determine the wavelengths of the given wave

When the frequency of the wave is $f_{a} = 100 H z$

The wavelength is determined by $λ_{a} f_{a} = c$
$\Rightarrow λ_{a} = \frac{c}{f_{a}} = \frac{3 \times 10^{8}}{100} = 3 \times 10^{6} m$

Similarly, for frequency $f_{b} = 1000 H z$

The wavelength is given as;

$λ_{b} = \frac{c}{f_{b}} = \frac{3 \times 10^{8}}{1000} = 3 \times 10^{5} m$

And, for frequency $f_{c} = 10, 000 H z$

The wavelength is given by;

$λ_{c} = \frac{c}{f_{c}} = \frac{3 \times 10^{8}}{10, 000} = 3 \times 10^{4} m$

Thus, it can be observed that $λ_{a} > λ_{b} > λ_{c}$
The largest wavelength is $λ_{a}$ and the smallest wavelength islocalid="1648817329905" $λ_{c}$ .

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Rank in order, from largest to smallest, the wavelengths $λ_{a}, λ_{b} a n d λ_{c}$ for sound waves having frequencies $f_{a} = 100 H z, f_{b} = 1000 H z, a n d f_{c} = 10, 000 H z$ . Explain.

Short Answer

Step by step solution

Step 1. Write the given information.

Step 2. To determine the wavelengths of the given wave

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Rank in order, from largest to smallest, the wavelengths λa,λbandλcfor sound waves having frequencies fa=100Hz,fb=1000Hz,andfc=10,000Hz. Explain.

Short Answer

Step by step solution

Step 1. Write the given information.

Step 2. To determine the wavelengths of the given wave

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Waves Physics

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Study anywhere. Anytime. Across all devices.

Rank in order, from largest to smallest, the wavelengths $λ_{a}, λ_{b} a n d λ_{c}$ for sound waves having frequencies $f_{a} = 100 H z, f_{b} = 1000 H z, a n d f_{c} = 10, 000 H z$ . Explain.