Dow University MDCAT / Entry Test Physics Waves — Set 3

Dow University MDCAT / Entry Test Physics Waves — Set 3

1. Question 1

   Q1. A wave with a frequency of 500 Hz travels at 340 m/s. Calculate its wavelength.

   • A) 0.68 m
   • B) 1.7 m
   • C) 340 m
   • D) 500 m

   Answer: 0.68 m

   Explanation: Use v = fλ. Option B fails because it incorrectly divides frequency by speed.

2. Question 2

   Q2. A tuning fork of 440 Hz produces ripples in water. If the wave speed is 0.88 m/s, find the period.

   • A) 0.0025 s
   • B) 0.002 s
   • C) 0.004 s
   • D) 0.003 s

   Answer: 0.0025 s

   Explanation: Period T = 1/f. Option C uses half the correct reciprocal.

3. Question 3

   Q3. A sonar pulse takes 0.2 s to return from a seabed. If sound travels at 1500 m/s in water, find the depth.

   • A) 150 m
   • B) 300 m
   • C) 750 m
   • D) 1500 m

   Answer: 150 m

   Explanation: Distance = (speed × time)/2. Option B ignores the round trip.

4. Question 4

   Q4. Two sound sources emit frequencies of 440 Hz and 438 Hz. Calculate the beat frequency.

   • A) 1.0 Hz
   • B) 2.0 Hz
   • C) 439 Hz
   • D) 876 Hz

   Answer: 2.0 Hz

   Explanation: Beat frequency = |f₁ - f₂|. Option A calculates half the correct value.

5. Question 5

   Q5. A sound wave has an intensity of 10⁻⁶ W/m². Calculate its decibel level (I₀ = 10⁻¹² W/m²).

   • A) 60 dB
   • B) 70 dB
   • C) 80 dB
   • D) 90 dB

   Answer: 60 dB

   Explanation: β = 10 log(I/I₀). Option C adds 10 dB erroneously.

6. Question 6

   Q6. A string fixed at both ends vibrates in its third harmonic at 120 Hz. What is its fundamental frequency?

   • A) 40 Hz
   • B) 60 Hz
   • C) 80 Hz
   • D) 120 Hz

   Answer: 40 Hz

   Explanation: Third harmonic is 3f₀. Option B divides by 2 instead of 3.

7. Question 7

   Q7. A car moving at 20 m/s emits a 500 Hz horn. If the speed of sound is 340 m/s, find the observed frequency by a stationary listener.

   • A) 531.25 Hz
   • B) 476.47 Hz
   • C) 540 Hz
   • D) 480 Hz

   Answer: 531.25 Hz

   Explanation: Use Doppler formula f' = f(v/(v - vs)). Option B applies denominator + vs.

8. Question 8

   Q8. A wave travels 240 m in 10 seconds. If its frequency is 6 Hz, calculate the wavelength.

   • A) 4 m
   • B) 6 m
   • C) 8 m
   • D) 10 m

   Answer: 4 m

   Explanation: v = distance/time. λ = v/f. Option B reverses v and f.

9. Question 9

   Q9. Two coherent waves interfere with path difference of 3λ/2. What is the resultant amplitude if both have amplitude A?

   • A) 0
   • B) A
   • C) 2A
   • D) √2A

   Answer: 0

   Explanation: Destructive interference occurs at odd multiples of λ/2. Option C assumes constructive.

10. Question 10

    Q10. A wave has a wavelength of 2 m and frequency 4 Hz. Calculate its period.

    • A) 0.5 s
    • B) 0.25 s
    • C) 2 s
    • D) 0.4 s

    Answer: 0.25 s

    Explanation: Period T = 1/f. Option A confuses frequency with wavelength.

11. Question 11

    Q11. A wave equation is y = 0.05 sin(2π(x/0.25 - t/0.01)). Calculate its frequency.

    • A) 100 Hz
    • B) 50 Hz
    • C) 25 Hz
    • D) 12.5 Hz

    Answer: 100 Hz

    Explanation: Frequency = 1/(time period in equation). Option B halves the correct value.

12. Question 12

    Q12. A standing wave in a 2 m string has 4 nodes. Calculate the wavelength.

    • A) 1.0 m
    • B) 1.33 m
    • C) 2.0 m
    • D) 4.0 m

    Answer: 1.33 m

    Explanation: Nodes divide the string into (n-1) segments. Option A assumes 3 nodes.

13. Question 13

    Q13. If the intensity of a sound increases 1000 times, its decibel level increases by:

    • A) 10 dB
    • B) 30 dB
    • C) 100 dB
    • D) 1000 dB

    Answer: 30 dB

    Explanation: β = 10 log(I₂/I₁). Option A assumes a 10-fold increase.

14. Question 14

    Q14. A closed pipe resonates at 250 Hz. Calculate the next higher resonant frequency.

    • A) 750 Hz
    • B) 500 Hz
    • C) 1000 Hz
    • D) 1250 Hz

    Answer: 750 Hz

    Explanation: Closed pipes have odd harmonics only. Option B skips to even.

15. Question 15

    Q15. Two waves have amplitudes 3 cm and 4 cm. Calculate their resultant amplitude if they are in phase.

    • A) 1 cm
    • B) 5 cm
    • C) 7 cm
    • D) 12 cm

    Answer: 7 cm

    Explanation: Constructive interference adds amplitudes. Option B uses Pythagorean sum.

16. Question 16

    Q16. A wave has a speed of 150 m/s and frequency of 50 Hz. Calculate its wavelength.

    • A) 3 m
    • B) 5 m
    • C) 7.5 m
    • D) 10 m

    Answer: 3 m

    Explanation: λ = v/f. Option B uses v = fλ incorrectly as v = f + λ.

17. Question 17

    Q17. A sound source moving away at 30 m/s emits 1000 Hz. Calculate observed frequency (speed of sound = 340 m/s).

    • A) 923 Hz
    • B) 1085 Hz
    • C) 941 Hz
    • D) 1058 Hz

    Answer: 923 Hz

    Explanation: Use Doppler formula f' = f(v/(v + vs)). Option C uses numerator - vs.

18. Question 18

    Q18. A wave has 5 crests in 2 seconds. Calculate its frequency.

    • A) 2.5 Hz
    • B) 2 Hz
    • C) 5 Hz
    • D) 0.4 Hz

    Answer: 2.5 Hz

    Explanation: Frequency = number of waves per second. Option B counts 4 waves.

19. Question 19

    Q19. A wave equation y = 0.1 sin(πx - 2πt) has a wave speed of:

    • A) 0.5 m/s
    • B) 1 m/s
    • C) 2 m/s
    • D) 4 m/s

    Answer: 2 m/s

    Explanation: Speed = ω/k. Option A uses k/ω instead.

20. Question 20

    Q20. A string of length 1.5 m has a fundamental frequency of 100 Hz. Calculate the wave speed.

    • A) 150 m/s
    • B) 300 m/s
    • C) 450 m/s
    • D) 600 m/s

    Answer: 300 m/s

    Explanation: v = 2Lf. Option A assumes length is half the wavelength.