how do you determine the velocity of a wave

HESI A2

HESI A2 Physics

1. How do you determine the velocity of a wave?

A. Multiply the frequency by the wavelength.
B. Add the frequency and the wavelength.
C. Subtract the wavelength from the frequency.
D. Divide the wavelength by the frequency.

Correct answer: A

Rationale: The velocity of a wave can be determined by multiplying the frequency of the wave by the wavelength. This relationship is given by the formula: velocity = frequency × wavelength. By multiplying the frequency by the wavelength, you can calculate the speed at which the wave is traveling. This formula is derived from the basic wave equation v = f × λ, where v represents velocity, f is frequency, and λ is wavelength. Therefore, to find the velocity of a wave, one must multiply its frequency by its wavelength. Choices B, C, and D are incorrect. Adding, subtracting, or dividing the frequency and wavelength does not yield the correct calculation for wave velocity. The correct formula for determining wave velocity is to multiply the frequency by the wavelength.

2. Faraday's law of electromagnetic induction states that a changing magnetic field in a conductor induces a/an:

A. Increase in resistance
B. Electromotive force
C. Static electric charge
D. Decrease in capacitance

Correct answer: B

Rationale: Faraday's law of electromagnetic induction states that a changing magnetic field induces an electromotive force in a conductor. This electromotive force is responsible for generating electricity in power plants and various electrical devices. The induced current is a result of the changing magnetic field, not an increase in resistance (choice A), static electric charge (choice C), or a decrease in capacitance (choice D). Hence, the correct answer is B.

3. When a gas is compressed isothermally, we can say that:

A. The gas performs work on the surroundings, and its internal energy increases.
B. The gas performs work on the surroundings, and its internal energy decreases.
C. The surroundings perform work on the gas, and its internal energy increases.
D. The surroundings perform work on the gas, and its internal energy decreases.

Correct answer: D

Rationale: When a gas is compressed isothermally, the surroundings perform work on the gas. In this process, since the temperature remains constant (isothermal), the internal energy of the gas does not change. Therefore, the correct answer is that the surroundings perform work on the gas, and its internal energy decreases. Choices A, B, and C are incorrect because they incorrectly describe the direction of work and the change in internal energy during an isothermal compression.

4. If a wave has a frequency of 60 hertz, which of the following is true?

A. It completes one cycle per minute.
B. It measures 60 m from crest to crest.
C. It completes 60 cycles per second.
D. It measures 60 m from crest to trough.

Correct answer: C

Rationale: The frequency of a wave is the number of cycles it completes in one second. A wave with a frequency of 60 hertz completes 60 cycles per second. Therefore, choice C is correct. Choice A is incorrect because a frequency of 60 hertz means 60 cycles per second, not per minute. Choice B is incorrect as the frequency of the wave does not determine the distance from crest to crest. Choice D is also incorrect as the frequency does not relate to the distance from crest to trough.

5. A 1,000-kg car drives at 10 m/s around a circle with a radius of 50 m. What is the centripetal acceleration of the car?

A. 2 m/s²
B. 4 m/s²
C. 5 m/s²
D. 10 m/s²

Correct answer: A

Rationale: Centripetal acceleration is calculated using the formula a = v² / r, where v = 10 m/s and r = 50 m. Substituting these values: a = (10 m/s)² / 50 m = 100 / 50 = 2 m/s². Therefore, the correct answer is 2 m/s². Choice B, 4 m/s², is incorrect because it is not the result of the correct calculation. Choice C, 5 m/s², is incorrect as it does not match the calculated centripetal acceleration. Choice D, 10 m/s², is incorrect as it does not reflect the correct calculation based on the given values.