College Physics
11th Edition
ISBN: 9781305952300
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
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12. Two waves travel at the same speed. The frequency of wave A is 1000 Hz, and the frequency of wave B is 4000 Hz. Wavelength A is
A. one-quarter the length of wavelength B.
B. one-half the length of wavelength B.
C. equal to the length of wavelength B.
D. four times the length of wavelength B.
![**Question 12:**
**Two waves travel at the same speed. The frequency of wave A is 1000 Hz, and the frequency of wave B is 4000 Hz. Wavelength A is:**
- A. one-quarter the length of wavelength B.
- B. one-half the length of wavelength B.
- C. equal to the length of wavelength B.
- D. four times the length of wavelength B.
**Explanation:**
This problem involves understanding the relationship between wave speed, frequency, and wavelength. The speed of a wave is given by the formula:
\[ \text{Speed} = \text{Frequency} \times \text{Wavelength} \]
Since both waves travel at the same speed, we can set up the equations for each wave and compare the wavelengths:
Let:
- \( f_A = 1000 \, \text{Hz} \)
- \( f_B = 4000 \, \text{Hz} \)
- \( \lambda_A \) and \( \lambda_B \) be the wavelengths of waves A and B, respectively.
Since the speeds are equal:
\[ f_A \times \lambda_A = f_B \times \lambda_B \]
Substitute the given frequencies:
\[ 1000 \times \lambda_A = 4000 \times \lambda_B \]
Solving for \( \lambda_A \):
\[ \lambda_A = 4 \lambda_B \]
Thus, wavelength A is four times the length of wavelength B, making the correct answer:
- **D. four times the length of wavelength B.**](https://content.bartleby.com/qna-images/question/6f0a8c67-ba07-4933-95fd-7d397a6626d9/cc4247ff-75f2-424e-871c-c11834429ed2/2z962m_processed.png)
Transcribed Image Text:**Question 12:**
**Two waves travel at the same speed. The frequency of wave A is 1000 Hz, and the frequency of wave B is 4000 Hz. Wavelength A is:**
- A. one-quarter the length of wavelength B.
- B. one-half the length of wavelength B.
- C. equal to the length of wavelength B.
- D. four times the length of wavelength B.
**Explanation:**
This problem involves understanding the relationship between wave speed, frequency, and wavelength. The speed of a wave is given by the formula:
\[ \text{Speed} = \text{Frequency} \times \text{Wavelength} \]
Since both waves travel at the same speed, we can set up the equations for each wave and compare the wavelengths:
Let:
- \( f_A = 1000 \, \text{Hz} \)
- \( f_B = 4000 \, \text{Hz} \)
- \( \lambda_A \) and \( \lambda_B \) be the wavelengths of waves A and B, respectively.
Since the speeds are equal:
\[ f_A \times \lambda_A = f_B \times \lambda_B \]
Substitute the given frequencies:
\[ 1000 \times \lambda_A = 4000 \times \lambda_B \]
Solving for \( \lambda_A \):
\[ \lambda_A = 4 \lambda_B \]
Thus, wavelength A is four times the length of wavelength B, making the correct answer:
- **D. four times the length of wavelength B.**
![**Physics Question on Waves**
**Question 12:**
*Two waves travel at the same speed. The frequency of wave A is 1000 Hz, and the frequency of wave B is 4000 Hz. Wavelength A is:*
- **A.** one-quarter the length of wavelength B.
- **B.** one-half the length of wavelength B.
- **C.** equal to the length of wavelength B.
- **D.** four times the length of wavelength B.
**Explanation:**
To solve this problem, use the relationship between wave speed (v), frequency (f), and wavelength (λ):
\[ v = f \times \lambda \]
Given that both waves travel at the same speed, we have:
\[ v_A = v_B \]
Therefore:
\[ f_A \times \lambda_A = f_B \times \lambda_B \]
Substituting the given frequencies:
\[ 1000 \times \lambda_A = 4000 \times \lambda_B \]
Solving for \(\lambda_A\):
\[ \lambda_A = \frac{4000}{1000} \times \lambda_B = 4 \times \lambda_B \]
Thus, wavelength A is four times the length of wavelength B.
**Correct Answer: D.** four times the length of wavelength B.](https://content.bartleby.com/qna-images/question/6f0a8c67-ba07-4933-95fd-7d397a6626d9/cc4247ff-75f2-424e-871c-c11834429ed2/da9e08o_processed.png)
Transcribed Image Text:**Physics Question on Waves**
**Question 12:**
*Two waves travel at the same speed. The frequency of wave A is 1000 Hz, and the frequency of wave B is 4000 Hz. Wavelength A is:*
- **A.** one-quarter the length of wavelength B.
- **B.** one-half the length of wavelength B.
- **C.** equal to the length of wavelength B.
- **D.** four times the length of wavelength B.
**Explanation:**
To solve this problem, use the relationship between wave speed (v), frequency (f), and wavelength (λ):
\[ v = f \times \lambda \]
Given that both waves travel at the same speed, we have:
\[ v_A = v_B \]
Therefore:
\[ f_A \times \lambda_A = f_B \times \lambda_B \]
Substituting the given frequencies:
\[ 1000 \times \lambda_A = 4000 \times \lambda_B \]
Solving for \(\lambda_A\):
\[ \lambda_A = \frac{4000}{1000} \times \lambda_B = 4 \times \lambda_B \]
Thus, wavelength A is four times the length of wavelength B.
**Correct Answer: D.** four times the length of wavelength B.
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