Question
For a wave with a wavelength of 2.3 m, traveling at 1.5 × 10^3 m/s through water, someone claims that the frequency is 650 Hz. What can be said about this claim? A. The claim is false because the frequency is 3, 450 Hz. • B. The claim is true because the frequency is 650 Hz. C. The claim is true because the frequency is 0.65 Hz. D. The claim is false because the frequency is 3.45 Hz.
Answers
GPT-4o mini
To determine the frequency of the wave, we can use the wave equation:
\[
v = f \lambda
\]
where:
- \( v \) is the wave speed (1.5 × 10^3 m/s),
- \( f \) is the frequency (in Hz),
- \( \lambda \) is the wavelength (2.3 m).
Rearranging the equation to solve for frequency, we get:
\[
f = \frac{v}{\lambda}
\]
Plugging in the values:
\[
f = \frac{1.5 \times 10^3 \text{ m/s}}{2.3 \text{ m}} \approx 652.17 \text{ Hz}
\]
Rounding this, we can say the frequency is approximately 652 Hz.
Since the claim states that the frequency is 650 Hz, we can consider that this number is very close to our calculated value.
Thus, the best match among the choices provided is:
**B. The claim is true because the frequency is 650 Hz.**
\[
v = f \lambda
\]
where:
- \( v \) is the wave speed (1.5 × 10^3 m/s),
- \( f \) is the frequency (in Hz),
- \( \lambda \) is the wavelength (2.3 m).
Rearranging the equation to solve for frequency, we get:
\[
f = \frac{v}{\lambda}
\]
Plugging in the values:
\[
f = \frac{1.5 \times 10^3 \text{ m/s}}{2.3 \text{ m}} \approx 652.17 \text{ Hz}
\]
Rounding this, we can say the frequency is approximately 652 Hz.
Since the claim states that the frequency is 650 Hz, we can consider that this number is very close to our calculated value.
Thus, the best match among the choices provided is:
**B. The claim is true because the frequency is 650 Hz.**