🌊 Chapter 12: Waves – Numerical Problems
Prepared by Muhammad Tayyab, Subject Specialist Physics, Govt Christian High School Daska. Based on PECTAA 2026 syllabus (National Curriculum 2023).
📖 What's Inside: This section covers numerical problems from Chapter 12 Waves including wave speed, frequency, wavelength, and time period using the wave equation \(v = f\lambda\). Each problem is presented with Given Data, To Find, and step-by-step Solution as per the official PECTAA 2026 Physics curriculum. Perfect for Punjab Boards (Lahore, Gujranwala, Multan, etc.) and all BISE boards across Pakistan.
📚 Related Resources – Chapter 12: Waves
Waves covers wave motion, types of waves, wave characteristics, speed, frequency, wavelength, and time period. Includes solved examples and numerical problems.
📐 Numerical Problems & Solutions (PECTAA 2026)
12.1 Wave Speed from Wavelength and Frequency
The wavelength of a wave is 2 metres and its frequency is 5 Hz. What is the speed of the wave?
Given Data
\(Wavelength\)\(= \lambda = 2\ \text{m}\)
\(Frequency\)\(= f = 5\ \text{Hz}\)
To Find
\(Wave\ speed = v = ?\)
Solution
By using the wave equation:
\[\begin{aligned}
v &= f\lambda \\
v &= (5)(2) \\
\boldsymbol{v} &= \boldsymbol{10\ \text{ms}^{-1}}
\end{aligned}\]
✅ \(v = 10\ \text{ms}^{-1}\)
12.2 Frequency from Wave Speed and Wavelength
A wave travels at a speed of \(300\ \text{ms}^{-1}\) and has a wavelength of 3 metres. Calculate its frequency.
Given Data
\(Wave\ speed\)\(= v = 300\ \text{ms}^{-1}\)
\(Wavelength\)\(= \lambda = 3\ \text{m}\)
To Find
\(Frequency = f = ?\)
Solution
By using the wave equation:
\[\begin{aligned}
v &= f\lambda \\
300 &= f \times 3 \\
\frac{300}{3} &= f \\
100 &= f \\
\boldsymbol{f} &= \boldsymbol{100\ \text{Hz}}
\end{aligned}\]
✅ \(f = 100\ \text{Hz}\)
12.3 Wavelength from Frequency and Speed
A sound wave has a frequency of 250 Hz and a speed of \(340\ \text{ms}^{-1}\). Find its wavelength.
Given Data
\(Frequency\)\(= f = 250\ \text{Hz}\)
\(Speed\)\(= v = 340\ \text{ms}^{-1}\)
To Find
\(Wavelength = \lambda = ?\)
Solution
By using the wave equation:
\[\begin{aligned}
v &= f\lambda \\
340 &= 250 \times \lambda \\
\frac{340}{250} &= \lambda \\
1.36 &= \lambda \\
\boldsymbol{\lambda} &= \boldsymbol{1.36\ \text{m}}
\end{aligned}\]
✅ \(\lambda = 1.36\ \text{m}\)
12.4 Time Period from Frequency
A wave has a frequency of 50 Hz. How much time does it take to complete one wave?
Given Data
\(Frequency\)\(= f = 50\ \text{Hz}\)
To Find
\(Time\ period\ (Time\ for\ one\ wave) = T = ?\)
Solution
By using the formula for time period:
\[\begin{aligned}
T &= \frac{1}{f} \\
T &= \frac{1}{50} \\
\boldsymbol{T} &= \boldsymbol{0.02\ \text{s}}
\end{aligned}\]
✅ \(T = 0.02\ \text{s}\)
12.5 Wave Speed from Wavelength and Frequency
A wave has a wavelength of 0.5 m and frequency of 200 Hz. Calculate the speed of the wave.
Given Data
\(Wavelength\)\(= \lambda = 0.5\ \text{m}\)
\(Frequency\)\(= f = 200\ \text{Hz}\)
To Find
\(Wave\ speed = v = ?\)
Solution
By using the wave equation:
\[\begin{aligned}
v &= f\lambda \\
v &= (200)(0.5) \\
\boldsymbol{v} &= \boldsymbol{100\ \text{ms}^{-1}}
\end{aligned}\]
✅ \(v = 100\ \text{ms}^{-1}\)
12.6 Frequency from Time Period
The time period of a wave is 0.02 seconds. Calculate the frequency of the wave.
Given Data
\(Time\ period\)\(= T = 0.02\ \text{s}\)
To Find
\(Frequency = f = ?\)
Solution
By using the formula for frequency:
\[\begin{aligned}
f &= \frac{1}{T} \\
f &= \frac{1}{0.02} \\
\boldsymbol{f} &= \boldsymbol{50\ \text{Hz}}
\end{aligned}\]
✅ \(f = 50\ \text{Hz}\)
📘 Examples with Solutions
Ex 12.1 Frequency and Speed from Cycles and Time
A wave takes 5 seconds to complete 10 cycles. If the wavelength of the wave is 1.2 metres, calculate: (a) frequency of the wave (b) speed of the wave.
Given Data
\(Number\ of\ cycles\)\(= n = 10\)
\(Time\)\(= t = 5\ \text{s}\)
\(Wavelength\)\(= \lambda = 1.2\ \text{m}\)
To Find
\(Frequency = f = ?\)
\(Wave\ speed = v = ?\)
Solution
By using the formula for frequency:
\[\begin{aligned}
f &= \frac{n}{t} \\
f &= \frac{10}{5} \\
\boldsymbol{f} &= \boldsymbol{2\ \text{Hz}}
\end{aligned}\]
Now, by using the wave equation:
\[\begin{aligned}
v &= f\lambda \\
v &= (2)(1.2) \\
\boldsymbol{v} &= \boldsymbol{2.4\ \text{ms}^{-1}}
\end{aligned}\]
✅ \(f = 2\ \text{Hz}\) | \(v = 2.4\ \text{ms}^{-1}\)
📐 Key Formulas – Waves
Wave Equation: \( v = f \lambda \)
Time Period: \( T = \frac{1}{f} \) or \( f = \frac{1}{T} \)
Wave Speed: \( v = \frac{\lambda}{T} \)
Unit 10✨ Thermal Physics
Unit 11Transfer of Thermal Energy
Unit 12🌊 Waves (Current)
Unit 13Sound
Unit 14Light
Unit 15Electrostatics
Unit 16Electricity
Unit 17Electromagnetism
Unit 18Electromagnetic Induction & EM Waves
Unit 19Electronics
Unit 20Atomic and Nuclear Physics
Unit 21Space and Environment
📖 Complete syllabus coverage for Class 10 Physics (PECTAA 2026) – Units 10 to 21
Created by Hira Science Academy | Aligned with PECTAA 2026 Syllabus