Relate Wavelength Frequency Wave Speed - Physics

1. What happens to wavelength $\lambda$ if $v$ is constant and frequency $f$ doubles?

   $\lambda$ halves. Since $\lambda=\frac{v}{f}$, doubling $f$ halves $\lambda$.

2. Calculate $\lambda$ if $v = 20\,\text{m}\,\text{s}^{-1}$ and $f = 4\,\text{Hz}$.

   $\lambda = 5\,\text{m}$. Apply $\lambda = \frac{v}{f} = \frac{20}{4} = 5$.

3. Calculate $f$ if $v=3\,\text{m}\,\text{s}^{-1}$ and $\lambda=0.25\,\text{m}$.

   $f=12\,\text{Hz}$. Using $f=\frac{v}{\lambda}$: $f=\frac{3}{0.25}=12\,\text{Hz}$.

4. Identify the SI unit of frequency $f$.

   hertz $(\text{Hz})$. Frequency measures cycles per second.

5. Calculate $v$ if $f=0.5\,\text{Hz}$ and $\lambda=8\,\text{m}$.

   $v=4\,\text{m}\,\text{s}^{-1}$. Using $v=f\lambda$: $v=0.5\times^8=4\,\text{m}\,\text{s}^{-1}$.

6. Identify the proportionality between $f$ and $\lambda$ when $v$ is constant.

   $f \propto \frac{1}{\lambda}$. Inverse proportionality when $v$ is constant.

7. Calculate $\lambda$ if $v = 1.5\,\text{m}\,\text{s}^{-1}$ and $f = 6\,\text{Hz}$.

   $\lambda = 0.25\,\text{m}$. Apply $\lambda = \frac{v}{f} = \frac{1.5}{6} = 0.25$.

8. Calculate $f$ if $v=12\,\text{m}\,\text{s}^{-1}$ and $\lambda=3\,\text{m}$.

   $f=4\,\text{Hz}$. Using $f=\frac{v}{\lambda}$: $f=\frac{12}{3}=4\,\text{Hz}$.

9. Identify the SI unit for wavelength $\lambda$.

   $\text{m}$. Wavelength is a distance measurement.

10. Identify the SI unit of wave speed $v$.

    $\text{m}\,\text{s}^{-1}$. Meters per second for velocity.

11. Find $\lambda$ if $f = 25\,\text{Hz}$ and $v = 5\,\text{m}\,\text{s}^{-1}$.

    $\lambda = 0.20\,\text{m}$. Apply $\lambda = \frac{v}{f} = \frac{5}{25} = 0.20$.

12. What happens to frequency $f$ if wave speed $v$ is constant and wavelength $\lambda$ triples?

    $f$ becomes $\frac{1}{3}$ as large. Since $v = f\lambda$ is constant, tripling $\lambda$ divides $f$ by 3.

13. What happens to wavelength $\lambda$ if wave speed $v$ is constant and frequency $f$ doubles?

    $\lambda$ halves. Since $v = f\lambda$ is constant, doubling $f$ halves $\lambda$.

14. What is the rearranged formula for wavelength $\lambda$ in terms of $v$ and $f$?

    $\lambda = \frac{v}{f}$. Rearrange $v = f\lambda$ by dividing both sides by $f$.

15. Identify the SI unit of wavelength $\lambda$.

    meter $(\text{m})$. Wavelength measures distance between wave peaks.

16. Find and correct the formula error: $v=\frac{f}{\lambda}$.

    Correct: $v=f\lambda$. The formula incorrectly divides; it should multiply $f$ and $\lambda$.

17. Find and correct the formula error: $\lambda=\frac{f}{v}$.

    Correct: $\lambda=\frac{v}{f}$. The formula has $f$ and $v$ swapped in the fraction.

18. Identify the SI unit for wave speed $v$.

    $\text{m}\,\text{s}^{-1}$. Meters per second is the standard unit for speed.

19. What happens to frequency $f$ if $v$ is constant and wavelength $\lambda$ triples?

    $f$ becomes $\frac{1}{3}$ as large. Since $f=\frac{v}{\lambda}$, tripling $\lambda$ divides $f$ by 3.

20. Calculate $v$ if $f=5\,\text{Hz}$ and $\lambda=2\,\text{m}$.

    $v=10\,\text{m}\,\text{s}^{-1}$. Using $v=f\lambda$: $v=5\times^2=10\,\text{m}\,\text{s}^{-1}$.

21. Find and correct the formula error: $v = \frac{\lambda}{f}$.

    Correct: $v = f\lambda$. The given formula incorrectly divides; multiply instead.

22. Calculate $v$ if $f = 0.5\,\text{Hz}$ and $\lambda = 8\,\text{m}$.

    $v = 4\,\text{m}\,\text{s}^{-1}$. Apply $v = f\lambda = 0.5 \times 8 = 4$.

23. Identify the SI unit for frequency $f$.

    $\text{Hz}$. Hertz means cycles per second.

24. Find $f$ if $\lambda = 0.80\,\text{m}$ and $v = 16\,\text{m}\,\text{s}^{-1}$.

    $f = 20\,\text{Hz}$. Apply $f = \frac{v}{\lambda} = \frac{16}{0.80} = 20$.

25. State the formula that relates wave speed $v$, frequency $f$, and wavelength $\lambda$.

    $v = f\lambda$. Wave speed equals frequency times wavelength.

26. Calculate $\lambda$ if $v=20\,\text{m}\,\text{s}^{-1}$ and $f=4\,\text{Hz}$.

    $\lambda=5\,\text{m}$. Using $\lambda=\frac{v}{f}$: $\lambda=\frac{20}{4}=5\,\text{m}$.

27. Calculate $\lambda$ if $v=1.5\,\text{m}\,\text{s}^{-1}$ and $f=6\,\text{Hz}$.

    $\lambda=0.25\,\text{m}$. Using $\lambda=\frac{v}{f}$: $\lambda=\frac{1.5}{6}=0.25\,\text{m}$.

28. Find $v$ if $f=250\,\text{Hz}$ and $\lambda=0.40\,\text{m}$.

    $v=100\,\text{m}\,\text{s}^{-1}$. Using $v=f\lambda$: $v=250\times^0.40=100\,\text{m}\,\text{s}^{-1}$.

29. Find $f$ if $v=60\,\text{m}\,\text{s}^{-1}$ and $\lambda=1.5\,\text{m}$.

    $f=40\,\text{Hz}$. Using $f=\frac{v}{\lambda}$: $f=\frac{60}{1.5}=40\,\text{Hz}$.

30. What happens to wave speed $v$ if frequency $f$ doubles and wavelength $\lambda$ halves?

    $v$ stays the same. Product $f\lambda$ remains constant: $2f \times \frac{\lambda}{2} = f\lambda$.

31. What happens to wave speed $v$ if $f$ doubles while $\lambda$ stays constant?

    $v$ doubles. Since $v=f\lambda$, doubling $f$ doubles $v$ when $\lambda$ is constant.

32. What is the rearranged formula for frequency $f$ in terms of $v$ and $\lambda$?

    $f = \frac{v}{\lambda}$. Rearrange $v = f\lambda$ by dividing both sides by $\lambda$.

33. Find $v$ if $\lambda = 0.40\,\text{m}$ and $f = 50\,\text{Hz}$.

    $v = 20\,\text{m}\,\text{s}^{-1}$. Apply $v = f\lambda = 50 \times 0.40 = 20$.

34. Calculate $v$ if $f = 5\,\text{Hz}$ and $\lambda = 2\,\text{m}$.

    $v = 10\,\text{m}\,\text{s}^{-1}$. Apply $v = f\lambda = 5 \times 2 = 10$.

35. Calculate $f$ if $v = 3\,\text{m}\,\text{s}^{-1}$ and $\lambda = 0.25\,\text{m}$.

    $f = 12\,\text{Hz}$. Apply $f = \frac{v}{\lambda} = \frac{3}{0.25} = 12$.

36. Find $\lambda$ if $v=340\,\text{m}\,\text{s}^{-1}$ and $f=170\,\text{Hz}$.

    $\lambda=2\,\text{m}$. Using $\lambda=\frac{v}{f}$: $\lambda=\frac{340}{170}=2\,\text{m}$.

37. Calculate $f$ if $v = 12\,\text{m}\,\text{s}^{-1}$ and $\lambda = 3\,\text{m}$.

    $f = 4\,\text{Hz}$. Apply $f = \frac{v}{\lambda} = \frac{12}{3} = 4$.

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