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.
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.
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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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.**](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6f0a8c67-ba07-4933-95fd-7d397a6626d9%2Fcc4247ff-75f2-424e-871c-c11834429ed2%2F2z962m_processed.png&w=3840&q=75)
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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6f0a8c67-ba07-4933-95fd-7d397a6626d9%2Fcc4247ff-75f2-424e-871c-c11834429ed2%2Fda9e08o_processed.png&w=3840&q=75)
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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