AP Entering The Park

Explanation
The speed of sound in air at 20 degrees Celsius is approximately 343 m/s. This means that your voice would have traveled at this speed as it traveled from one side of the tunnel to the other.

Explanation
The fundamental frequency of a tunnel can be calculated using the formula: f = v/2L, where f is the frequency, v is the speed of sound, and L is the length of the tunnel. Plugging in the values, we get f = 345/(2*30.5) = 5.66 Hz.

Explanation
The second harmonic of a frequency is twice the frequency, and the third harmonic is three times the frequency. Therefore, if the given frequencies are the second and third harmonics of the tunnel, then the original frequency of the tunnel must be half of the second harmonic and one-third of the third harmonic. By dividing 11.3 Hz by 2, we get 5.65 Hz, which is close to 5.66 Hz. By dividing 17.0 Hz by 3, we get 5.67 Hz, which is close to 5.66 Hz. Therefore, the second and third harmonics of the tunnel are 11.3 Hz and 17.0 Hz respectively.

Explanation
As the car approaches you, the frequency of the sound waves that reach your ears is higher than the actual frequency emitted by the car. This is due to the Doppler effect, which causes an increase in frequency when the source of sound is moving towards the observer. The formula to calculate the observed frequency is: observed frequency = actual frequency * (speed of sound + speed of observer) / (speed of sound + speed of source). Plugging in the given values, we get: observed frequency = 800 Hz * (343 m/s + 25 m/s) / (343 m/s + 0 m/s) = 863 Hz.

Explanation
As the car moves away from you, the frequency of the sound waves emitted by the horn appears to decrease. This is due to the Doppler effect, which causes a shift in frequency when there is relative motion between the source of the sound waves and the observer. The formula to calculate the observed frequency is f' = f * (v + v_o) / (v + v_s), where f is the frequency of the source, v is the speed of sound, v_o is the speed of the observer, and v_s is the speed of the source. Plugging in the given values, we get f' = 800 * (343 + 0) / (343 + 25) = 746 Hz. Therefore, the correct answer is 746 Hz.

Explanation
When the ring is tossed horizontally, it will follow a projectile motion. The horizontal velocity does not affect the vertical motion, so the time taken to reach the ground can be calculated using the equation:

time = √(2h/g)

where h is the initial height (1 m) and g is the acceleration due to gravity (9.8 m/s^2).

Substituting the values, we get:

time = √(2*1/9.8) = √(0.204) ≈ 0.452 s

The horizontal distance traveled can be calculated using the equation:

distance = velocity * time

Substituting the given velocity (2 m/s) and the calculated time, we get:

distance = 2 * 0.452 ≈ 0.904 m

Therefore, the ring will travel approximately 0.904 m.

Explanation
The "taffy" constant represents the elasticity of the taffy. It is calculated by dividing the force applied (300 N) by the distance stretched (15 cm), giving a value of 20 N/m. However, the given answer is 2000 N/m, which is incorrect.

Explanation
The angle of refraction for the quarter is 35.1 degrees. This can be determined using Snell's law, which states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the indices of refraction of the two mediums. In this case, the angle of incidence is 50 degrees and the index of refraction for water is 1.333. By rearranging the equation and solving for the angle of refraction, we find that it is 35.1 degrees.

Explanation
When looking at oneself in a plane mirror, the image formed is virtual, meaning it cannot be projected onto a screen. The image is also upright, meaning it appears in the same orientation as the object being reflected. Lastly, the image is the same size as the object, as plane mirrors produce a reflection that is a one-to-one ratio with the object's size.

Explanation
When you see your image inverted in a concave mirror, it indicates that your face is located outside the focal point of the mirror. In a concave mirror, the focal point is the point where parallel rays of light converge after reflection. If your face were located at the focal point or inside it, the reflected rays would not converge and your image would not be inverted. Therefore, the correct answer is outside the focal point.