Date: 202101
Local time of day: 1201-1800
Location: TOA.Airport, CA
Flight conditions: VMC
Weather elements / visibility: 50
Light: Daylight
Aircraft: Small Aircraft
Operator: FBO
Operating under: Part 91
Flight plan: IFR
Mission: Training
Flight phase: Initial Climb
Airspace: Class D TOA; Class E SCT
ATC / advisory: TRACON SCT
Second aircraft: Any Unknown or Unlisted Aircraft Manufacturer
Reporter organization: FBO
Reporter function: Pilot Not Flying; Instructor
Reporter qualification: Flight Crew Multiengine; Flight Crew Flight Instructor; Flight Crew Commercial; Flight Crew Instrument
Human factors: Communication Breakdown; Situational Awareness
Anomaly: ATC Issue All Types; Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Clearance; Inflight Event / Encounter CFTT / CFIT
Detector: Person Air Traffic Control; Person Flight Crew
Result: Air Traffic Control Issued Advisory / Alert; Flight Crew Returned To Clearance; Flight Crew Took Evasive Action
Contributing factors: Human Factors
Primary problem: Human Factors

Narrative: Training flight on IFR Tower enroute clearance from TOA to ZZZ. Clearance was fly runway heading to intercept LAX 170 radial to LIMBO; V64; SLI; Direct. On departure from TOA my student was flying under the view-limiting device and I was pilot monitoring and looking outside for traffic. We departed Runway 29R; shortly after there was a departure from a parallel 29L of a light aircraft that was faster than our aircraft. While switching to Departure Control frequency we were advised of proximity of the overtaking aircraft and its altitude being same as ours. I was looking outside and was able to spot the aircraft in about 20 seconds and student flying advised ATC of us having visual contact. Another 20 seconds later I lost visual contact and took over controls momentarily using 3 step process to raise the left wing to check on the overtaking aircraft that was turning south at that time. I gave the controls back to my student using 3 step process. When my student was saying 'my controls' he blocked end of Controller's transmission for me. The part that I heard was only 'turn left 150.' Then; student read back 'Turn left 150 Aircraft X' and initiated a left turn to 150. At that time I started to question myself if this instruction could really be intended to us since it would probably put us below the MVA in the area. I clearly heard my student's readback to ATC about left turn to 150 and since Controller didn't say anything about his read back being wrong; I thought I shouldn't probably even worry. Just a moment later; because of the oddness of the situation I decided to clarify the instruction with the ATC; but by the time I was able to key the mic; Controller already was getting back to us questioning our actions. Only then I realized that my student responded to a call intended to another aircraft and Controller didn't even hear his readback because the transmission was blocked by the radio call of the aircraft that really received that instruction.I think contributing factors to this little misunderstanding was our scratchy radio. Because of it the student misheard the call sign and I couldn't even hear it; due to intercom on that particular plane being clearer than the radio and student was talking at the same time.Good thing there was no conflicting traffic and VMC conditions let me see the terrain.




Synopsis: GA flight instructor reported a track heading deviation resulting in a CFTT event during departure from TOA airport.  Reporter stated they inadvertently took a heading clearance intended for another aircraft.