Question
The wavelength of a sound wave traveling through air increases by a factor of 5 as it begins traveling
through metal. An observer notes that the frequency of the sound does not change. What is true about
the speed of the wave? (1 point)
Answers below:
The speed increases by a factor of 5.
The speed is equal to the speed of light.
The speed decreases by a factor of 5.
The speed does not change.
through metal. An observer notes that the frequency of the sound does not change. What is true about
the speed of the wave? (1 point)
Answers below:
The speed increases by a factor of 5.
The speed is equal to the speed of light.
The speed decreases by a factor of 5.
The speed does not change.
Answers
There are no human answers yet.
Answered by
GPT-4o mini
The speed of a wave is determined by the equation:
\[ v = f \lambda \]
where \( v \) is the wave speed, \( f \) is the frequency, and \( \lambda \) is the wavelength.
Since the frequency (\( f \)) does not change and the wavelength (\( \lambda \)) increases by a factor of 5 when the sound wave travels through metal, we can analyze the situation as follows:
Let the initial wavelength in air be \( \lambda_0 \), making the initial speed of sound in air:
\[ v_0 = f \lambda_0 \]
When the sound wave moves into metal, the new wavelength becomes \( \lambda = 5\lambda_0 \). Since the frequency remains constant, the new speed in metal can be expressed as:
\[ v = f (5 \lambda_0) = 5 f \lambda_0 = 5 v_0 \]
This means the speed of the wave through the metal increases by a factor of 5.
Therefore, the answer is:
**The speed increases by a factor of 5.**
\[ v = f \lambda \]
where \( v \) is the wave speed, \( f \) is the frequency, and \( \lambda \) is the wavelength.
Since the frequency (\( f \)) does not change and the wavelength (\( \lambda \)) increases by a factor of 5 when the sound wave travels through metal, we can analyze the situation as follows:
Let the initial wavelength in air be \( \lambda_0 \), making the initial speed of sound in air:
\[ v_0 = f \lambda_0 \]
When the sound wave moves into metal, the new wavelength becomes \( \lambda = 5\lambda_0 \). Since the frequency remains constant, the new speed in metal can be expressed as:
\[ v = f (5 \lambda_0) = 5 f \lambda_0 = 5 v_0 \]
This means the speed of the wave through the metal increases by a factor of 5.
Therefore, the answer is:
**The speed increases by a factor of 5.**
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